bluuebunny/crossref_metadata_2025 huggingface dataset:
An equilibrium validation technique based on Bayesian inference
Authors: Hole M.J. , von Nessi G. , Svensson J. , Appel L.C.
Published: August 2011

In recent years, Bayesian probability theory has been used in a number of experiments to fold uncertainties and interdependences in the diagnostic data and forward models, and together with prior knowledge of the state of the plasma, thus increase accuracy of inferred physics variables. Key developments include the application to current and flux surface tomography, effective charge, the electron energy distribution function, neutron spectrometry and density. Virtual observations have also been introduced to better constrain inferred quantities in current tomography. In this work we present Bayesian inference results of toroidal and poloidal current and flux surface tomography. Whilst the uncertainty in these profiles, as well as the uncertainty in inferred parameters such as the safety factor profile is small (<5%), the inference can change substantially depending on the physics model used. We also present Bayesian inference results for Thomson scattering and charge-exchange recombination spectroscopy. In separate work we have computed radial force balance components on the midplane in the Mega Ampére Spherical tokamak. Our aim is to establish a validation framework for different equilibrium physics models. We find that in the overlapping region of the core (normalized poloidal flux less than 0.4) and motional Stark effect (MSE) chords, the plasma is consistent with static Grad–Shafranov force balance to within two standard deviations. In the outboard edge region, where MSE data are also available, the pressure gradient exceeds the Lorentz force. Most likely, this is because the poloidal current is not constrained to zero at the plasma edge. To lowest order, the results suggest computing components of force balance are useful to assess data-consistency, independent of any equilibrium solution. To first order, we have integrated the residue to force balance to infer an energetic particle pressure.
Reply to comment on ‘Lost in translation: topological singularities in group field theory’
Authors: Gurau Razvan
Published: August 2011

In Smerlak (2011 Class. Quantum. Grav.
28 178001) the author disputes the conclusion of our paper (Gurau 2010 Class. Quantum Grav.
27 235023). He claims that the Feynman graphs of three-dimensional group field theory always represent pseudo-manifolds. However,

Smerlak (2011) uses a different definition for pseudo-manifolds.

In order to apply the new definition Smerlak (2011) proposes a construction which cannot be implemented in a path integral by Feynman rules.

These two points invalidate the claims of Smerlak (2011).
On the converse to a theorem of Atiyah and Bott
Authors: Friedman Robert , Morgan John
Published: August 2011

Let

G
G

be a complex reductive group and let

C
C

be a smooth curve of genus at least one. We prove a converse to a theorem of Atiyah-Bott concerning the stratification of the space of holomorphic

G
G

-bundles on

C
C

. In case the genus of

C
C

is one, we establish that there is a stratification in the strong sense. The paper concludes with a characterization of the minimally unstable strata in case

G
G

is simple
F-regular and F-pure rings vs. log terminal and log canonical singularities
Authors: Hara Nobuo , Watanabe Kei-ichi
Published: August 2011

We investigate the relationship of F-regular (resp. F-pure) rings and log terminal (resp. log canonical) singularities. Also, we extend the notions of F-regularity and F-purity to “F-singularities of pairs." The notions of F-regular and F-pure rings in characteristic

p
>
0

p > 0

are characterized by a splitting of the Frobenius map, and define some classes of rings having “mild" singularities. On the other hand, there are notions of log terminal and log canonical singularities defined via resolution of singularities in characteristic zero. These are defined also for pairs of a normal variety and a

Q

\mathbb Q

-divisor on it, and play important roles in birational algebraic geometry. As an analog of these singularities of pairs, we introduce the concept of “F-singularities of pairs," namely strong F-regularity, divisorial F-regularity and F-purity for a pair

(
A
,
Δ
)

(A,\Delta )

of a normal ring

A
A

of characteristic

p
>
0

p > 0

and an effective

Q

\mathbb Q

-divisor

Δ
\Delta

on

Spec
⁡
A

\operatorname {Spec} A

. The main theorem of this paper asserts that, if

K

A

+
Δ

K_{A}+\Delta

is

Q

\mathbb Q

-Cartier, then the above three variants of F-singularities of pairs imply KLT, PLT and LC properties, respectively. We also prove some results for F-singularities of pairs which are analogous to singularities of pairs in characteristic zero.
The action of the Frobenius map on rank 2 vector bundles in characteristic 2
Authors: Laszlo Y. , Pauly C.
Published: August 2011

We compute the rational morphism of “inverse image by Frobenius” acting on the coarse moduli space of semi-stable rank

2
2

bundles of trivial determinant over an ordinary genus curve in characteristic

2
2

.
On the structure of Selmer groups over 𝑝-adic Lie extensions
Authors: Ochi Yoshihiro , Venjakob Otmar
Published: August 2011

The goal of this paper is to prove that the Pontryagin dual of the Selmer group over the trivializing extension of an elliptic curve without complex multiplication does not have any nonzero pseudo-null submodule. The main point is to extend the definition of pseudo-null to modules over the completed group ring

Z

p

[
[
G
]
]

\mathbb {Z}_p[[G]]

of an arbitrary

p
p

-adic Lie group

G
G

without

p
p

-torsion. For this purpose we prove that

Z

p

[
[
G
]
]

\mathbb {Z}_p[[G]]

is an Auslander regular ring. For the proof we also extend some results of Jannsen’s homotopy theory of modules and study intensively higher Iwasawa adjoints.
A reconstruction of Euler data
Authors: Lian Bong , Liu Chien-Hao , Yau Shing-Tung
Published: August 2011

We apply the mirror principle (see Mirror principle, I, Asian J. Math. 1 (1997), pp. 729–763) to reconstruct the Euler data

Q
=
{

Q
d

}

d
∈

N

∪
{
0
}

Q=\{Q_d\}_{d\in {\mathbb N}\cup \{0\}}

associated to a vector bundle

V
V

on

C

P

n

{\mathbb C}{\mathrm P}^n

and a multiplicative class

b
b

. This gives a direct way to compute the intersection number

K
d

K_d

without referring to any other Euler data linked to

Q
Q

. Here

K
d

K_d

is the integral of the cohomology class

b
(

V
d

)

b(V_d)

of the induced bundle

V
d

V_d

on a stable map moduli space. A package “EulerData_MP.m” in Maple V that carries out the actual computation is provided in the electronic version math.AG/0003071 of the current paper. For

b
b

, the Chern polynomial, the computation of

K
1

K_1

for the bundle

V
=

T

∗

C

P

2

V=T_{\ast }{\mathbb C}{\mathrm P}^2

, and

K
d

K_d

,

d
=
1
,
2
,
3

d=1,2,3

, for the bundles

O

C

P

4

(
l
)

{\mathcal O}_{{\mathbb C}{\mathrm P}^4}(l)

with

6
≤
l
≤
10

6\le l\le 10

are done using the code and are also included.
The theory of Coleman power series for 𝐾₂
Authors: Fukaya Takako
Published: August 2011

The purpose of this paper is to define “Coleman power series” associated to norm compatible systems in

K
2

K_2

groups of complete discrete valuation fields of mixed characteristic

(
0
,
p
)

(0,p)

with imperfect residue fields

k

{\mathsf {k}}

such that

[

k

:

k

p

]
=
p

[{\mathsf {k}}:{\mathsf {k}}^p]=p

. These “Coleman power series” are elements of

K
2

K_2

groups of certain power series rings. We use our “Coleman power series” to obtain some results on modular forms, and we also study properties of our “Coleman power series”.
Mirror symmetry of abelian varieties and multi-theta functions
Authors: Fukaya Kenji
Published: August 2011

We study homological mirror symmetry conjecture of symplectic and complex torus. We will associate a mirror torus(T2n,ω+−1B)∧(T^{2n},\omega +\sqrt {-1}B)^{\wedge }to each symplectic torus(T2n,ω)(T^{2n},\omega )together with a closed 2 formBBwhich we call aBB-field. We will associate a coherent sheafE(L,L){\mathcal E}(L,{\mathcal L})on(T2n,ω+−1B)∧(T^{2n},\omega +\sqrt {-1}B)^{\wedge }to each pair(L,L)(L,{\mathcal L})of affine Lagrangian submanifoldsLLand a flat complex line bundleL{\mathcal L}onLL. In the case of affine Lagrangian submanifolds, we show that the Floer homology of Langrangian submanifolds is isomorphic to the extension of the mirror sheafE(L,L){\mathcal E}(L,{\mathcal L}). We construct a canonical isomorphism in the case when a certain transversality condition is satisfied. Our isomorphism then is functorial.
Group representations and the Euler characteristic of elliptically fibered Calabi–Yau threefolds
Authors: Grassi Antonella , Morrison David
Published: August 2011

To every elliptic Calabi–Yau threefold with a section

X
X

there can be associated a Lie group

G
G

and a representation

ρ
\rho

of that group, determined from the Weierstrass model and the types of singular fibers. We explain this construction, which first arose in physics. The requirement of anomaly cancellation in the associated physical theory makes some surprising predictions about the connection between

X
X

and

ρ
\rho

, including an explicit formula (in terms of

ρ
\rho

) for the Euler characteristic of

X
X

. We give a purely mathematical proof of that formula in this paper, introducing along the way a new invariant of elliptic Calabi–Yau threefolds. We also verify the other geometric predictions which are consequences of anomaly cancellation, under some mild hypotheses. As a byproduct we discover a novel relation between the Coxeter number and the rank in the case of the simply laced groups in the “exceptional series” studied by Deligne.
On the moduli of stable sheaves on some nonreduced projective schemes
Authors: Inaba Michi-aki
Published: August 2011

We study the moduli space of stable sheaves on a projective scheme whose structure sheaf has a nilpotent ideal with some property. We introduce a stratification on this moduli space. Each stratum is the moduli space of some extensions of sheaves. This stratification is described on a curve with multiple structure and on a double plane, and the structure of each stratum is studied. In the case of a curve with multiple structure, we also study a local structure of the moduli space of stable sheaves.
Sur la cohomologie de la puissance symétrique du fibré tautologique sur le schéma de Hilbert ponctuel d’une surface
Authors: Danila Gentiana
Published: August 2011

We compute some cohomology spaces for the symmetric power of the tautological bundle tensor the determinant bundle on the punctual Hilbert scheme

X

[
n
]

X^{\mbox {}^{[n]}}

of a smooth projective surface

X
X

on

C

{\mathbb C}

.
Corrigendum to “Realization of Voevodsky’s motives”
Authors: Huber A.
Published: August 2011

One key aim of the author [Realization of Voevodsky’s motives, J. Algebraic Geom. 9 (2000), no. 4, 755–799] was to construct a realization functor from Voevodsky’s triangulated category of geometrical motives to her own triangulated category of mixed realizations. This note corrects a mistake in this construction. The new argument consists of a rearrangement of the original construction together with a careful analysis of hypercovers of complexes of varieties.
Cubic threefolds and abelian varieties of dimension five
Authors: Casalaina-Martin Sebastian , Friedman Robert
Published: August 2011

This paper proves the following converse to a theorem of Mumford: Let

A
A

be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular point, and suppose that the multiplicity of the singular point is three. Then

A
A

is isomorphic as a principally polarized abelian variety to the intermediate Jacobian of a smooth cubic threefold. The method of proof is to analyze the possible singularities of the theta divisor of

A
A

, and ultimately to show that

A
A

is the Prym variety of a possibly singular plane quintic.
Connectedness of Hilbert schemes
Authors: Peeva Irena , Stillman Mike
Published: August 2011

We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over an exterior algebra, is connected. We give a new proof of Hartshorne’s Theorem that the classical Hilbert scheme is connected. More precisely: if

Q
Q

is either a polynomial ring or an exterior algebra, we prove that every two strongly stable ideals in

Q
Q

with the same Hilbert function are connected by a sequence of binomial Gröbner deformations.
The closed topological vertex via the Cremona transform
Authors: Bryan Jim , Karp Dagan
Published: August 2011

We compute the local Gromov-Witten invariants of the “closed vertex”, that is, a configuration of three

P

1

\mathbb {P}^{1}

’s meeting in a single triple point in a Calabi-Yau threefold. The method is to express the local invariants of the vertex in terms of ordinary Gromov-Witten invariants of a certain blowup of

P

3

\mathbb {P}^{3}

and then to compute those invariants via the geometry of the Cremona transformation.
Log-terminal singularities and vanishing theorems via non-standard tight closure
Authors: Schoutens Hans
Published: August 2011

Generalizing work of Smith and Hara, we give a new characterization of log-terminal singularities for finitely generated algebras over

C

\mathbb C

, in terms of purity properties of ultraproducts of characteristic

p
p

Frobenii. As a first application we obtain a Boutot-type theorem for log-terminal singularities: given a pure morphism

Y
→
X

Y\to X

between affine

Q

\mathbb Q

-Gorenstein varieties of finite type over

C

\mathbb C

, if

Y
Y

has at most log-terminal singularities, then so does

X
X

. The second application is the Vanishing for Maps of Tor for log-terminal singularities: if

A
⊆
R

A\subseteq R

is a Noether Normalization of a finitely generated

C

\mathbb C

-algebra

R
R

and

S
S

is an

R
R

-algebra of finite type with log-terminal singularities, then the natural morphism

Tor
i
A

⁡
(
M
,
R
)
→

Tor
i
A

⁡
(
M
,
S
)

\operatorname {Tor}^A_i(M,R) \to \operatorname {Tor}^A_i(M,S)

is zero, for every

A
A

-module

M
M

and every

i
≥
1

i\geq 1

. The final application is Kawamata-Viehweg Vanishing for a connected projective variety

X
X

of finite type over

C

\mathbb C

whose affine cone has a log-terminal vertex (for some choice of polarization). As a corollary, we obtain a proof of the following conjecture of Smith: if

G
G

is the complexification of a real Lie group acting algebraically on a projective smooth Fano variety

X
X

, then for any numerically effective line bundle

L

\mathcal L

on any GIT quotient

Y
:=
X

/

/

G

Y:=X/\!/G

, each cohomology module

H
i

(
Y
,

L

)

H^i(Y,\mathcal L)

vanishes for

i
>
0

i>0

, and, if

L

\mathcal L

is moreover big, then

H
i

(
Y
,

L

−
1

)

H^i(Y,\mathcal L^{-1})

vanishes for

i
>
dim
⁡
Y

i>\operatorname {dim}Y

.
Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces
Authors: Viehweg Eckart , Zuo Kang
Published: August 2011

Let

M

d
,
n

\mathcal {M}_{d,n}

be the moduli stack of hypersurfaces

X
⊂

P

n

X \subset \mathbb {P}^n

of degree

d
≥
n
+
1

d\geq n+1

, and let

M

d
,
n

(
1
)

\mathcal M_{d,n}^{(1)}

be the sub-stack, parameterizing hypersurfaces obtained as a

d
d

-fold cyclic covering of

P

n
−
1

\mathbb {P}^{n-1}

ramified over a hypersurface of degree

d
d

. Iterating this construction, one obtains

M

d
,
n

(
ν
)

\mathcal {M}_{d,n}^{(\nu )}

. We show that

M

d
,
n

(
1
)

\mathcal {M}_{d,n}^{(1)}

is rigid in

M

d
,
n

\mathcal {M}_{d,n}

, although for

d
>
2
n

d>2n

the Griffiths-Yukawa coupling degenerates. However, for all

d
≥
n
+
1

d\geq n+1

the sub-stack

M

d
,
n

(
2
)

\mathcal {M}^{(2)}_{d,n}

deforms. We calculate the exact length of the Griffiths-Yukawa coupling over

M

d
,
n

(
ν
)

\mathcal {M}_{d,n}^{(\nu )}

, and we construct a

4
4

-dimensional family of quintic hypersurfaces

g
:

Z

→
T

g:\mathcal {Z}\to T

in

P

4

\mathbb {P}^4

, and a dense set of points

t
t

in

T
T

, such that

g

−
1

(
t
)

g^{-1}(t)

has complex multiplication.
Fibrations, divisors and transcendental leaves
Authors: Pereira Jorge
Published: August 2011

We use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of fibrations, the topology of smooth hypersurfaces, and the topological closure of transcendental leaves of foliations.
Geometric proofs of Horn and saturation conjectures
Authors: Belkale Prakash
Published: August 2011

We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also establish transversality theorems for Schubert calculus in nonzero characteristic.
On quasi-reductive group schemes
Authors: Prasad Gopal , Yu Jiu-Kang
Published: August 2011

This paper was motivated by a question of Vilonen, and the main results have been used by Mirković and Vilonen to give a geometric interpretation of the dual group (as a Chevalley group over

Z

)

\mathbb {Z})

of a reductive group. We define a quasi-reductive group over a discrete valuation ring

R
R

to be an affine flat group scheme over

R
R

such that (i) the fibers are of finite type and of the same dimension; (ii) the generic fiber is smooth and connected, and (iii) the identity component of the reduced special fiber is a reductive group. We show that such a group scheme is of finite type over

R
R

, the generic fiber is a reductive group, the special fiber is connected, and the group scheme is smooth over

R
R

in most cases, for example when the residue characteristic is not 2, or when the generic fiber and reduced special fiber are of the same type as reductive groups. We also obtain results about group schemes over a Dedekind scheme or a Noetherian scheme. We show that in residue characteristic 2 there are non-smooth quasi-reductive group schemes with generic fiber

SO

2
n
+
1

\operatorname {SO}_{2n+1}

and they can be classified when

R
R

is strictly Henselian.
Degenerations of surface scrolls and the Gromov-Witten invariants of Grassmannians
Authors: Coskun Izzet
Published: August 2011

We describe an algorithm for computing certain characteristic numbers of rational normal surface scrolls using degenerations. As a corollary we obtain an efficient method for computing the corresponding Gromov-Witten invariants of the Grassmannians of lines.
Desingularization of toric and binomial varieties
Authors: Bierstone Edward , Milman Pierre
Published: August 2011

We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-up with smooth invariant centres that satisfy the normal flatness condition of Hironaka. The results extend to more general varieties defined locally by binomial equations.
Stability manifold of ℙ¹
Authors: Okada So
Published: August 2011

We describe the stability manifold of the bounded derived category

D
⁡
(

P

1

)

\operatorname {D}(\mathbb {P}^{1})

of coherent sheaves on

P

1

\mathbb {P}^{1}

, denoted

Stab
⁡
(
D
⁡
(

P

1

)
)

\operatorname {Stab}(\operatorname {D}(\mathbb {P}^{1}))

.
Type II unprojection
Authors: Papadakis Stavros
Published: August 2011

Answering a question of M. Reid, we define and prove the Gorensteiness of the type II unprojection.
A tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces
Authors: Shustin Eugenii
Published: August 2011

The Welschinger invariants of real rational algebraic surfaces are natural analogues of the genus zero Gromov-Witten invariants. We establish a tropical formula to calculate the Welschinger invariants of real toric Del Pezzo surfaces for any conjugation-invariant configuration of points. The formula expresses the Welschinger invariants via the total multiplicity of certain tropical curves (non-Archimedean amoebas) passing through generic configurations of points, and then via the total multiplicity of some lattice paths in the convex lattice polygon associated with a given surface. We also present the results of computation of Welschinger invariants, obtained jointly with I. Itenberg and V. Kharlamov.
Iwasawa theory of the fine Selmer group
Authors: Wuthrich Christian
Published: August 2011

The fine Selmer group of an elliptic curve

E
E

over a number field

K
K

is obtained as a subgroup of the usual Selmer group by imposing stronger conditions at places above

p
p

. We prove a formula for the Euler-characteristic of the fine Selmer group over a

Z

p

\mathbb {Z}_p

-extension and use it to compute explicit examples.
La singularité de O’Grady
Authors: Lehn Manfred , Sorger Christoph
Published: August 2011

Let

M

2
v

M_{2v}

be the moduli space of semistable sheaves with Mukai vector

2
v

2v

on an abelian or

K
3

K3

surface where

v
v

is primitive such that

⟨
v
,
v
⟩
=
2

\langle v,v \rangle =2

. We show that the blow-up of the reduced singular locus of

M

2
v

M_{2v}

provides a symplectic resolution of singularities. This provides a direct description of O’Grady’s resolutions of

M

K
3

(
2
,
0
,
4
)

M_{K3}(2,0,4)

and

M

A
b

(
2
,
0
,
2
)

M_{Ab}(2,0,2)

.

Résumé. Soit

M

2
v

M_{2v}

l’espace de modules des faisceaux semi-stables de vecteur de Mukai

2
v

2v

sur une surface

K
3

K3

ou abélienne où

v
v

est primitif tel que

⟨
v
,
v
⟩
=
2

\langle v,v \rangle =2

. Nous montrons que l’éclatement de

M

2
v

M_{2v}

le long de son lieu singulier réduit fournit une résolution symplectique des singularités. Ceci donne une description directe des résolutions de O’Grady de

M

K
3

(
2
,
0
,
4
)

M_{K3}(2,0,4)

et

M

A
b

(
2
,
0
,
2
)

M_{Ab}(2,0,2)

.
The Witten top Chern class via 𝐾-theory
Authors: Chiodo Alessandro
Published: August 2011

The Witten top Chern class is the crucial cohomology class needed to state a conjecture by Witten relating the Gelfand–Dikiĭ hierarchies to higher spin curves. In the paper by Polishchuk and Vaintrob (Contemp. Math., vol. 276, Amer. Math. Soc., 2001, pp. 229–249) an algebraic construction of such a class is provided. We present a more straightforward construction via

K
K

-theory. In this way we short-circuit the passage through bivariant intersection theory and the use of MacPherson’s graph construction. Furthermore, we show that the Witten top Chern class admits a natural lifting to the

K
K

-theory ring.
Compactification of the moduli space of hyperplane arrangements
Authors: Hacking Paul , Keel Sean , Tevelev Jenia
Published: August 2011

Consider the moduli space

M
0

M^0

of arrangements of

n
n

hyperplanes in general position in projective

(
r
−
1
)

(r-1)

-space. When

r
=
2

r=2

the space has a compactification given by the moduli space of stable curves of genus

0
0

with

n
n

marked points. In higher dimensions, the analogue of the moduli space of stable curves is the moduli space of stable pairs: pairs

(
S
,
B
)

(S,B)

consisting of a variety

S
S

(possibly reducible) and a divisor

B
=

B
1

+
⋯
+

B
n

B=B_1+\dots +B_n

, satisfying various additional conditions. We identify the closure of

M
0

M^0

in the moduli space of stable pairs as Kapranov’s Hilbert quotient compactification of

M
0

M^0

, and give an explicit description of the pairs at the boundary. We also construct additional irreducible components of the moduli space of stable pairs.
The generalized de Rham-Witt complex over a field is a complex of zero-cycles
Authors: Rülling Kay
Published: August 2011

Bloch and Esnault defined additive higher Chow groups with modulus

m
m

on the level of zero cycles over a field

k
k

denoted by
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="CH Superscript n Baseline left-parenthesis left-parenthesis double-struck upper A Subscript k Superscript 1 Baseline comma left-parenthesis m plus 1 right-parenthesis StartSet 0 EndSet right-parenthesis comma n minus 1 right-parenthesis">

CH
n

(
(

A

k
1

,
(
m
+
1
)
{
0
}
)
,
n
−
1
)

\text {CH}^n((\mathbb {A}^1_k,(m+1)\{0\}),n-1)

,

n
,
m
≥
1

n,m\ge 1

. Bloch and Esnault prove
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="CH Superscript n Baseline left-parenthesis left-parenthesis double-struck upper A Subscript k Superscript 1 Baseline comma 2 StartSet 0 EndSet right-parenthesis comma n minus 1 right-parenthesis approximately-equals normal upper Omega Subscript k slash double-struck upper Z Superscript n minus 1">

CH
n

(
(

A

k
1

,
2
{
0
}
)
,
n
−
1
)
≅

Ω

k

/

Z

n
−
1

\text {CH}^n((\mathbb {A}^1_k,2\{0\}),n-1)\cong \Omega ^{n-1}_{k/\mathbb {Z}}

. In this paper we generalize their result and prove that the additive Chow groups with higher modulus form a generalized Witt complex over

k
k

and are as such isomorphic to the generalized de Rham-Witt complex of Bloch-Deligne-Hesselholt-Illusie-Madsen.
Intersection cohomology of hypertoric varieties
Authors: Proudfoot Nicholas , Webster Benjamin
Published: August 2011

A hypertoric variety is a quaternionic analogue of a toric variety. Just as the topology of toric varieties is closely related to the combinatorics of polytopes, the topology of hypertoric varieties interacts richly with the combinatorics of hyperplane arrangements and matroids. Using finite field methods, we obtain combinatorial descriptions of the Betti numbers of hypertoric varieties, both for ordinary cohomology in the smooth case and intersection cohomology in the singular case. We also introduce a conjectural ring structure on the intersection cohomology of a hypertoric variety.
Images of extended period maps
Authors: Usui Sampei
Published: August 2011

As a geometric application of polarized log Hodge structures, we show the following. Let

M

H

s
m

M_{H}^{\mathrm {sm}}

be a projective variety which is a compactification of the coarse moduli space of surfaces of general type constructed by Kawamata, Kollár, Shepherd-Barron, Alexeev, Mori, Karu, et al., and let

Γ
∖

D

Σ

\Gamma \backslash D_{\Sigma }

be a log manifold which is the fine moduli space of polarized log Hodge structures constructed by Kato and Usui. If we take a suitable finite cover

M
′

→

M

i

M’\to M_{i}

of any irreducible component

M

i

M_{i}

of

M

H

s
m

M_{H}^{\mathrm {sm}}

, and if we assume the existence of a suitable fan

Σ
\Sigma

, then there is an extended period map

ψ
:

M
′

→
Γ
∖

D

Σ

\psi :M’\to \Gamma \backslash D_{\Sigma }

and its image is the analytic subspace associated to a separated compact algebraic space. The point is that, although

Γ
∖

D

Σ

\Gamma \backslash D_{\Sigma }

is a “log manifold” with slits, the image

ψ
(

M
′

)

\psi (M’)

is not affected by these slits and is a classical familiar object: a separated compact algebraic space.
Lagrangian fibrations on Hilbert schemes of points on K3 surfaces
Authors: Sawon Justin
Published: August 2011

Let

H
i
l
b

g

S

\mathrm {Hilb}^gS

be the Hilbert scheme of

g
g

points on a K3 surface

S
S

. Suppose that

P
i
c

S
≅

Z

C

\mathrm {Pic}S\cong \mathbb {Z}C

where

C
C

is a smooth curve with

C
2

=
2
(
g
−
1
)

n
2

C^2=2(g-1)n^2

. We prove that

H
i
l
b

g

S

\mathrm {Hilb}^gS

is a Lagrangian fibration.
An analogue of the field-of-norms functor and of the Grothendieck conjecture
Authors: Abrashkin Victor
Published: August 2011

The paper contains a construction of an analogue of the Fontaine-Wintenberger field-of-norms functor for higher-dimensional local fields. This construction is done completely in terms of the ramification theory of such fields. It is applied to deduce the mixed characteristic case of a local analogue of the Grothendieck conjecture for these fields from its characteristicppcase, which was proved earlier by the author.
A finiteness theorem for the Brauer group of abelian varieties and 𝐾3 surfaces
Authors: Skorobogatov Alexei , Zarhin Yuri
Published: August 2011

Let

k
k

be a field finitely generated over the field of rational numbers, and

Br
⁡
(
k
)

\operatorname {Br}(k)

the Brauer group of

k
k

. For an algebraic variety

X
X

over

k
k

we consider the cohomological Brauer–Grothendieck group

Br
⁡
(
X
)

\operatorname {Br}(X)

. We prove that the quotient of

Br
⁡
(
X
)

\operatorname {Br}(X)

by the image of

Br
⁡
(
k
)

\operatorname {Br}(k)

is finite if

X
X

is a

K
3

K3

surface. When

X
X

is an abelian variety over

k
k

, and

X
¯

\overline {X}

is the variety over an algebraic closure

k
¯

\overline {k}

of

k
k

obtained from

X
X

by the extension of the ground field, we prove that the image of

Br
⁡
(
X
)

\operatorname {Br}(X)

in

Br
⁡
(

X
¯

)

\operatorname {Br}(\overline {X})

is finite.
Moduli spaces of 𝑝-divisible groups
Authors: Viehmann Eva
Published: August 2011

We study the global structure of moduli spaces of quasi-isogenies ofpp-divisible groups introduced by Rapoport and Zink. We determine their dimensions and their sets of connected components and of irreducible components. If the isocrystals of thepp-divisible groups are simple, we compute the cohomology of the moduli space. As an application we determine which moduli spaces are smooth.
A non-Archimedean analogue of the Hodge-𝒟-conjecture for products of elliptic curves
Authors: Sreekantan Ramesh
Published: August 2011

In this paper we show that the map\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="partial-differential colon upper C upper H squared left-parenthesis upper E 1 times upper E 2 comma 1 right-parenthesis circled-times double-struck upper Q long right-arrow upper P upper C upper H Superscript 1 Baseline left-parenthesis script upper X Subscript v Baseline right-parenthesis">∂:CH2(E1×E2,1)⊗Q⟶PCH1(Xv)\partial :CH^2(E_1 \times E_2,1)\otimes \mathbb {Q} \longrightarrow PCH^1(\mathcal {X}_v)\]is surjective, whereE1E_1andE2E_2are two non-isogenous semistable elliptic curves over a local field,CH2(E1×E2,1)CH^2(E_1 \times E_2,1)is one of Bloch’s higher Chow groups andPCH1(Xv)PCH^1(\mathcal {X}_v)is a certain subquotient of a Chow group of the special fibreXv\mathcal {X}_{v}of a semi-stable modelX\mathcal {X}ofE1×E2E_1 \times E_2. On one hand, this can be viewed as a non-Archimedean analogue of the Hodge-D\mathcal {D}-conjecture of Beilinson - which is known to be true in this case by the work of Chen and Lewis (J. Algebraic Geom.14(2005), 213–240), and on the other, an analogue of the works of Speiß (KK-Theory17(1999), 363–383), Mildenhall (Duke Math. J.67(1992), 387–406) and Flach (Invent. Math.109(1992), 307–327) in the case when the elliptic curves have split multiplicative reduction.
The degree of the discriminant of irreducible representations
Authors: Fehér L. , Némethi A. , Rimányi R.
Published: August 2011

We present a formula for the degree of the discriminant of irreducible representations of a Lie group, in terms of the roots of the group and the highest weight of the representation. The proof uses equivariant cohomology techniques, namely, the theory of Thom polynomials, and a new method for their computation. We study the combinatorics of our formulas in various special cases.
Toric vector bundles, branched covers of fans, and the resolution property
Authors: Payne Sam
Published: August 2011

We associate to each toric vector bundle on a toric variety

X
(
Δ
)

X(\Delta )

a “branched cover” of the fan

Δ
\Delta

together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric Cartier divisors and piecewise-linear functions. We apply this combinatorial geometric technique to investigate the existence of resolutions of coherent sheaves by vector bundles, using singular nonquasiprojective toric threefolds as a testing ground. Our main new result is the construction of complete toric threefolds that have no nontrivial toric vector bundles of rank less than or equal to three. The combinatorial geometric sections of the paper, which develop a theory of cone complexes and their branched covers, can be read independently.
Deformation classes of real four-dimensional cubic hypersurfaces
Authors: Finashin S. , Kharlamov V.
Published: August 2011

We study real nonsingular cubic hypersurfaces

X
⊂

P
5

X\subset P^5

up to deformation equivalence combined with projective equivalence and prove that they are classified by the conjugacy classes of involutions induced by the complex conjugation in

H
4

(
X
)

H_4(X)

. Moreover, we provide a graph

Γ

K
4

\Gamma _{K4}

whose vertices represent the equivalence classes of such cubics and whose edges represent their adjacency. It turns out that the graph

Γ

K
4

\Gamma _{K4}

essentially coincides with the graph

Γ

K
3

\Gamma _{K3}

characterizing a certain adjacency of real nonpolarized K3-surfaces.
The Pfaffian-Grassmannian derived equivalence
Authors: Borisov Lev , Căldăraru Andrei
Published: August 2011

We argue that there exists a derived equivalence between Calabi–Yau threefolds obtained by taking dual hyperplane sections (of the appropriate codimension) of the Grassmannian

G

(
2
,
7
)

\mathbf {G}(2,7)

and the Pfaffian

P
f

(
7
)

\mathbf {Pf}(7)

. The existence of such an equivalence has been conjectured by physicists for almost ten years, as the two families of Calabi–Yau threefolds are believed to have the same mirror. It is the first example of a derived equivalence between non-birational Calabi–Yau threefolds.
Continuity of volumes on arithmetic varieties
Authors: Moriwaki Atsushi
Published: August 2011

We introduce the volume function for

C

∞

C^{\infty }

-hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef

C

∞

C^{\infty }

-hermitian invertible sheaf. We also give other applications, for example, a generalized Hodge index theorem, an arithmetic Bogomolov-Gieseker’s inequality, etc.
Unstable blowups
Authors: Stoppa Jacopo
Published: August 2011

Let

(
X
,
L
)

(X,L)

be a polarised manifold. We show that K-stability and asymptotic Chow stability of the blowup of

X
X

along a

0
0

-dimensional cycle are closely related to Chow stability of the cycle itself, for polarisations making the exceptional divisors small. This can be used to give (almost) a converse to the results of Arezzo and Pacard (2004 and 2007) and to give new examples of Kähler classes with no constant scalar curvature representatives.
Low-dimensional singularities with free divisors as discriminants
Authors: Buchweitz Ragnar-Olaf , Ebeling Wolfgang , Graf von Bothmer Hans-Christian
Published: August 2011

We present versal complex analytic families, over a smooth base and of fibre dimension zero, one, or two, where the discriminant constitutes a free divisor. These families include finite flat maps, versal deformations of reduced curve singularities, and versal deformations of Gorenstein surface singularities in

C

5

\mathbb {C}^5

. It is shown that such free divisors often admit a “fast normalization”, obtained by a single application of the Grauert-Remmert normalization algorithm. For a particular Gorenstein surface singularity in

C

5

\mathbb {C}^5

, namely the simple elliptic singularity of type

A
~

4

\widetilde A_{4}

, we exhibit an explicit discriminant matrix and show that the slice of the discriminant for a fixed

j
j

-invariant is the cone over the dual variety of an elliptic curve.
Milnor 𝐾-theory of local rings with finite residue fields
Authors: Kerz Moritz
Published: August 2011

We propose a definition of improved Milnor

K
K

-groups of local rings with finite residue fields, such that the improved Milnor

K
K

-sheaf in the Zariski topology is a universal extension of the naive Milnor

K
K

-sheaf with a certain transfer map for étale extensions of local rings. The main theorem states that the improved Milnor

K
K

-ring is generated by elements of degree one.
Effective Iitaka fibrations
Authors: Viehweg Eckart , Zhang De-Qi
Published: August 2011

For every

n
n

-dimensional projective manifold

X
X

of Kodaira dimension

2
2

we show that

Φ

|

M

K
X

|

\Phi _{|M K_X|}

is birational to an Iitaka fibration for a computable positive integer

M
=
M
(
b
,

B

n
−
2

)

M = M(b, B_{n-2})

, where

b
>
0

b > 0

is minimal with

|

b

K
F

|

≠
∅

|bK_F| \ne \emptyset

for a general fibre

F
F

of an Iitaka fibration of

X
X

, and where

B

n
−
2

B_{n-2}

is the Betti number of a smooth model of the canonical

Z

/

(
b
)

\mathbb {Z}/(b)

-cover of the

(
n
−
2
)

(n-2)

-fold

F
F

. In particular,

M
M

is a universal constant if the dimension

n
≤
4

n \le 4

.
General isotropic flags are general (for Grassmannian Schubert calculus)
Authors: Sottile Frank
Published: August 2011

We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert varieties defined by such flags meet transversally. This strengthens a result of Belkale and Kumar.
Comparing powers and symbolic powers of ideals
Authors: Bocci Cristiano , Harbourne Brian
Published: August 2011

We develop tools to study the problem of containment of symbolic powersI(m)I^{(m)}in powersIrI^rfor a homogeneous idealIIin a polynomial ringk[PN]k[\textbf {P}^N]inN+1N+1variables over an arbitrary algebraically closed fieldkk. We obtain results on the structure of the set of pairs(r,m)(r,m)such thatI(m)⊆IrI^{(m)}\subseteq I^r. As corollaries, we show thatI2I^2containsI(3)I^{(3)}wheneverSSis a finite generic set of points inP2\textbf {P}^2(thereby giving a partial answer to a question of Huneke), and we show that the containment theorems of Ein–Lazarsfeld–Smith [Invent. Math. 144 (2001), pp. 241–252] and Hochster–Huneke [Invent. Math. 147 (2002), pp. 349–369] are optimal for every fixed dimension and codimension.
Addendum to “Semistable reduction of 𝐺-bundles on curves”
Authors: Heinloth Jochen
Published: August 2011

In this note we give a variation of the last step of the proof of the semistable reduction theorem of [J. Algebraic Geom. 17 (2008), 167–183], which allows us to remove the assumptions on the characteristic of the ground field.
Hilbert’s theorem on positive ternary quartics: A refined analysis
Authors: Scheiderer Claus
Published: August 2011

Let

X
X

be an integral plane quartic curve over a field

k
k

, let

f
f

be an equation for

X
X

. We first consider representations

(
∗
)

(*)

c
f
=

p
1

p
2

−

p
0
2

cf=p_1p_2-p_0^2

(where

c
∈

k
∗

c\in k^*

and the

p
i

p_i

are quadratic forms), up to a natural notion of equivalence. Using the general theory of determinantal varieties we show that equivalence classes of such representations correspond to nontrivial globally generated torsion-free rank one sheaves on

X
X

with a self-duality which are not exceptional, and that the exceptional sheaves are in bijection with the

k
k

-rational singular points of

X
X

. For

k
=

C

k=\mathbb {C}

, the number of representations

(
∗
)

(*)

(up to equivalence) depends only on the singularities of

X
X

, and is determined explicitly in each case. In the second part we focus on the case where

k
=

R

k=\mathbb {R}

and

f
f

is nonnegative. By a famous theorem of Hilbert, such

f
f

is a sum of three squares of quadratic forms. We use the Brauer group and Galois cohomology to relate identities

(
∗
∗
)

(**)

f
=

p
0
2

+

p
1
2

+

p
2
2

f=p_0^2+p_1^2+p_2^2

to

(
∗
)

(*)

, and we determine the number of equivalence classes of representations

(
∗
∗
)

(**)

for each

f
f

. Both in the complex and in the real definite case, our results are considerably more precise since they give the number of representations with any prescribed base locus.
Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology
Authors: Nicaise Johannes
Published: August 2011

We describe the homotopy type of the analytic Milnor fiber in terms of a strictly semi-stable model, and we show that its singular cohomology coincides with the weight zero part of the mixed Hodge structure on the nearby cohomology. We give a similar expression for Denef and Loeser’s motivic Milnor fiber in terms of a strictly semi-stable model.
Super-potentials for currents on compact Kähler manifolds and dynamics of automorphisms
Authors: Dinh Tien-Cuong , Sibony Nessim
Published: August 2011

We introduce a notion of super-potential (canonical function) associated to positive closed

(
p
,
p
)

(p,p)

-currents on compact Kähler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of deformations in the space of currents. As an application, we obtain several results on the dynamics of holomorphic automorphisms: regularity and uniqueness of the Green currents. We also get regularity, entropy, ergodicity and hyperbolicity of the equilibrium measures.
On the notion of geometry over 𝔽₁
Authors: Connes Alain , Consani Caterina
Published: August 2011

We refine the notion of variety over the “field with one element” developed by C. Soulé by introducing a grading in the associated functor to the category of sets, and show that this notion becomes compatible with the geometric viewpoint developed by J. Tits. We then solve an open question of C. Soulé by proving, using results of J. Tits and C. Chevalley, that Chevalley group schemes are examples of varieties over a quadratic extension of the above “field”.
Toward an inductive description of singularities of pairs
Authors: Mustaţă Mircea
Published: August 2011

Motivated by Shokurov’s ACC Conjecture for log canonical thresholds, we propose an inductive point of view on singularities of pairs, in the case when the ambient variety is smooth. Our main result characterizes the log canonicity of a pair in dimension

n
+
1

n+1

by the log canonicity of another pair (not effective, in general) in dimension

n
n

.
Proof of the main conjecture of noncommutative Iwasawa theory for totally real number fields in certain cases
Authors: Kakde Mahesh
Published: August 2011

Fix an odd primepp. LetGGbe a compactpp-adic Lie group containing a closed, normal, pro-ppsubgroupHHwhich is abelian and such thatG/HG/His isomorphic to the additive group ofpp-adic integersZp\mathbb {Z}_p. First we assume thatHHis finite and compute the Whitehead group of the Iwasawa algebra,λ(G)\lambda (G), ofGG. We also prove some results about certain localisation ofλ(G)\lambda (G)needed in Iwasawa theory. LetFFbe a totally real number field and letF∞F_{\infty }be an admissiblepp-adic Lie extension ofFFwith Galois groupGG. The computation of the Whitehead groups are used to show that the Main Conjecture for the extensionF∞/FF_{\infty }/Fcan be deduced from certain congruences between abelianpp-adic zeta functions of Deligne and Ribet. We prove these congruences with certain assumptions onGG. This gives a proof of the Main Conjecture in many interesting cases such asZp⋊Zp\mathbb {Z}_p\rtimes \mathbb {Z}_p-extensions.
A framework for analytical characterization of monoclonal antibodies based on reactivity profiles in different tissues
Authors: Rossin Elizabeth , Lin Tsung-I , Ho Hsiu J. , Mentzer Steven J. , Pyne Saumyadipta
Published: August 2011

Motivation: Monoclonal antibodies (mAbs) are among the most powerful and important tools in biology and medicine. MAb development is of great significance to many research and clinical applications. Therefore, objective mAb classification is essential for categorizing and comparing mAb panels based on their reactivity patterns in different cellular species. However, typical flow cytometric mAb profiles present unique modeling challenges with their non-Gaussian features and intersample variations. It makes accurate mAb classification difficult to do with the currently used kernel-based or hierarchical clustering techniques.

Results: To address these challenges, in the present study we developed a formal two-step framework called mAbprofiler for systematic, parametric characterization of mAb profiles. Further, we measured the reactivity of hundreds of new antibodies in diverse tissues using flow cytometry, which we successfully classified using mAbprofiler.

First, mAbprofiler fits a mAb's flow cytometric histogram with a finite mixture model of skew t distributions that is robust against non-Gaussian features, and constructs a precise, smooth and mathematically rigorous profile. Then it performs novel curve clustering of the fitted mAb profiles using a skew t mixture of non-linear regression model that can handle intersample variation. Thus, mAbprofiler provides a new framework for identifying robust mAb classes, all well defined by distinct parametric templates, which can be used for classifying new mAb samples. We validated our classification results both computationally and empirically using mAb profiles of known classification.

Availability and Implementation: A demonstration code in R is available at the journal website. The R code implementing the full framework is available from the author website – http://amath.nchu.edu.tw/www/teacher/tilin/software

Contact:  saumyadipta_pyne@dfci.harvard.edu

Supplementary Information:  Supplementary data are available at Bioinformatics online.
cSSMD: assessing collective activity for addressing off-target effects in genome-scale RNA interference screens
Authors: Zhang Xiaohua Douglas , Santini Francesca , Lacson Raul , Marine Shane D. , Wu Qian , Benetti Luca , Yang Ruojing , McCampbell Alex , Berger Joel P. , Toolan Dawn M. , Stec Erica M. , Holder Daniel J. , Soper Keith A. , Heyse Joseph F. , Ferrer Marc
Published: August 2011

Motivation: Off-target activity commonly exists in RNA interference (RNAi) screens and often generates false positives. Existing analytic methods for addressing the off-target effects are demonstrably inadequate in RNAi confirmatory screens.

Results: Here, we present an analytic method assessing the collective activity of multiple short interfering RNAs (siRNAs) targeting a gene. Using this method, we can not only reduce the impact of off-target activities, but also evaluate the specific effect of an siRNA, thus providing information about potential off-target effects. Using in-house RNAi screens, we demonstrate that our method obtains more reasonable and sensible results than current methods such as the redundant siRNA activity (RSA) method, the RNAi gene enrichment ranking (RIGER) method, the frequency approach and the t-test.

Contact:  xiaohua_zhang@merck.com

Supplementary information:  Supplementary data are available at Bioinformatics online.