pinecone/core-2020-05-10-deduplication huggingface dataset:
Star Configurations are Set-Theoretic Complete Intersections

Let $\mathcal A\subset\mathbb P^{k-1}$ be a rank $k$ arrangement of $n$
hyperplanes, with the property that any $k$ of the defining linear forms are
linearly independent (i.e., $\mathcal A$ is called $k-$generic). We show that
for any $j=0,\ldots,k-2$, the subspace arrangement with defining ideal
generated by the $(n-j)-$fold products of the defining linear forms of
$\mathcal A$ is a set-theoretic complete intersection, which is equivalent to
saying that star configurations have this property.Comment: 5 pages. In this version we present an update with an example
  answering negatively the question asked previously whether or not, for ANY
  hyperplane arrangement, all the ideals generated by a-fold products of the
  defining linear forms are set-theoretic complete intersection
A characterization of the $\hat{A}$-genus as a linear combination of
  Pontrjagin numbers

We show in this short note that if a rational linear combination of
Pontrjagin numbers vanishes on all simply-connected $4k$-dimensional closed
connected and oriented spin manifolds admitting a Riemannian metric whose Ricci
curvature is nonnegative and nonzero at any point, then this linear combination
must be a multiple of the $\hat{A}$-genus, which improves on a result of Gromov
and Lawson. Our proof combines an idea of Atiyah and Hirzebruch and the
celebrated Calabi-Yau theorem.Comment: 5 page
Base sizes of imprimitive linear groups and orbits of general linear
  groups on spanning tuples

For a subgroup $L$ of the symmetric group $S_\ell$, we determine the minimal
base size of $GL_d(q)\wr L$ acting on $V_d(q)^\ell$ as an imprimitive linear
group. This is achieved by computing the number of orbits of $GL_d(q)$ on
spanning $m$-tuples, which turns out to be the number of $d$-dimensional
subspaces of $V_m(q)$. We then use these results to prove that for certain
families of subgroups $L$, the affine groups whose stabilisers are large
subgroups of $GL_d(q)\wr L$ satisfy a conjecture of Pyber concerning bases.Comment: 8 page
Quantum j-invariant in positive characteristic I: Definition and
  Convergence

We introduce the quantum $j$-invariant in positive characteristic as a
multi-valued, modular-invariant function of a local function field. In this
paper, we concentrate on basic definitions and questions of convergence.
  Note: This version contains a correction to the published version of Theorem
3. The error that was found is not in any way serious, but its correction does
change slightly the statement of Theorem 3 appearing in the published version.
Otherwise, it has no impact on this article nor any of its sequels.Comment: 10 page
Essential dimension of algebraic groups, including bad characteristic

We give upper bounds on the essential dimension of (quasi-)simple algebraic
groups over an algebraically closed field that hold in all characteristics. The
results depend on showing that certain representations are generically free. In
particular, aside from the cases of spin and half-spin groups, we prove that
the essential dimension of a simple algebraic group $G$ of rank at least two is
at most $\mathrm{dim}(G) - 2(\mathrm{rank}(G)) - 1$. It is known that the
essential dimension of spin and half-spin groups grows exponentially in the
rank. In most cases, our bounds are as good or better than those known in
characteristic zero and the proofs are shorter. We also compute the generic
stabilizer of an adjoint group on its Lie algebra.Comment: v2 is a substantial revisio
Fourth-order Schr\"odinger type operator with singular potentials

In this paper we study the biharmonic operator perturbed by an inverse
fourth-order potential. In particular, we consider the operator
$A=\Delta^2-V=\Delta^2-c|x|^{-4}$ where $c$ is any constant such that
$c<\left(\frac{N(N-4)}{4}\right)^2$. The semigroup generated by $-A$ in
$L^2(\mathbb{R}^N)$, $N\geq5$, extrapolates to a bounded holomorphic
$C_0$-semigroup on $L^p(\mathbb{R}^N)$ for $p\in [p^{'}_0,p_0]$ where
$p_0=\frac{2N}{N-4}$ and $p_0^{'}$ is its dual exponent. Furthermore, we study
the boundedness of the Riesz transform $\Delta A^{-1/2}$ on $L^p(\mathbb{R}^N)$
for all $p\in(p_0^{'},2]$
On the exponent of the automorphism group of a compact Riemann surface

Let $X$ be a compact Riemann surface of genus $g\geq 2$, and let $Aut(X)$ be
its group of automorphims. We show that the exponent of $Aut(X)$ is bounded by
$42(g-1)$. We also determine explicitly the infinitely many values of $g$ for
which this bound is reached and the corresponding groups. Finally we discuss
related questions for subgroups $G$ of $Aut(X)$ that are subject to additional
conditions, for example being solvable.Comment: final version, 13 pages, several improvements thanks to the refere
Strange divisibility in groups and rings

We prove a general divisibility theorem that implies, e.g., that, in any
group, the number of generating pairs (as well as triples, etc.) is a multiple
of the order of the commutator subgroup. Another corollary says that, in any
associative ring, the number of Pythagorean triples (as well as four-tuples,
etc.) of invertible elements is a multiple of the order of the multiplicative
group.Comment: 7 pages. A Russian version of this paper is at
  http://halgebra.math.msu.su/staff/klyachko/papers.htm . V.2: misprints
  corrected, some applications generalised. V.3: minor additions and
  corrections. V.4: Some corrections and generalisations (see Theorem on
  Monomorphisms and Subgroups). V.5: A reference is adde
Finitely generated modules over quasi-Euclidean rings

Let R be a unital commutative ring and let $M$ be an $R$-module that is
generated by $k$ elements but not less. Let $E_n(R)$ be the subgroup of
$GL_n(R)$ generated by the elementary matrices. In this paper we study the
action of $E_n(R)$ by matrix multiplication on the set $Um_n(M)$ of unimodular
rows of $M$ of length $n \ge k$. Assuming $R$ is moreover Noetherian and
quasi-Euclidean, e.g., $R$ is a direct sum of finitely many Euclidean rings, we
show that this action is transitive if $n > k$. We also prove that $Um_k(M)
/E_k(R)$ is equipotent with the unit group of $R/(a_1)$ where $(a_1)$ is the
first invariant factor of $M$. These results encompass the well-known
classification of Nielsen non-equivalent generating tuples in finitely
generated Abelian groups.Comment: 7 pages, no figure. Results and proofs are unchanged. The
  modifications are the following: - one new reference - correction of a very
  confusing typo in Corollary C (the author thanks W. van der Kallen) -
  correction of two typos on page 6 (the author thanks D. Oancea
Born-Infeld solitons, Maximal surfaces and Ramanujan's identities

We show that a Born-Infeld soliton can be realised either as a spacelike
minimal graph or timelike minimal graph over a timelike plane or a combination
of both away from singular points. We also obtain some exact solutions of the
Born-Infeld equation from already known solutions to the maximal surface
equation. Further we present a method to construct a one-parameter family of
complex solitons from a given one parameter family of maximal surfaces.
Finally, using Ramanujan's Identities and the Weierstrass-Enneper
representation of maximal surfaces, we derive further non-trivial identities.Comment: 12 pages, published online in Archiv der Mathemati
Existence of Self-Cheeger sets on Riemannian manifolds

Let $(\mathcal{M},g)$ be a compact Riemannian manifold of dimension $N\geq
2$. We prove the existence of a family $(\Omega_\varepsilon)_{\varepsilon\in
(0,\varepsilon_0)}$ of self-Cheeger sets in $(\mathcal{M},g)$ . The domains
$\Omega_\varepsilon\subset\mathcal{M}$ are perturbations of geodesic balls of
radius $\varepsilon$ centered at $p \in \mathcal{M}$, and in particular, if
$p_0$ is a non-degenerate critical point of the scalar curvature of $g$, then
the family $(\partial \Omega_\varepsilon)_{\varepsilon \in (0,\varepsilon_0)}$
constitutes a smooth foliation of a neighborhood of $p_0$.Comment: Revised argument on section 2, Results unchanged. Published in Archiv
  der Mathemati
A commuting-vector-field approach to some dispersive estimates

We prove the pointwise decay of solutions to three linear equations: (i) the
transport equation in phase space generalizing the classical Vlasov equation,
(ii) the linear Schrodinger equation, (iii) the Airy (linear KdV) equation. The
usual proofs use explicit representation formulae, and either obtain
$L^1$---$L^\infty$ decay through directly estimating the fundamental solution
in physical space, or by studying oscillatory integrals coming from the
representation in Fourier space. Our proof instead combines "vector field"
commutators that capture the inherent symmetries of the relevant equations with
conservation laws for mass and energy to get space-time weighted energy
estimates. Combined with a simple version of Sobolev's inequality this gives
pointwise decay as desired. In the case of the Vlasov and Schrodinger equations
we can recover sharp pointwise decay; in the Schrodinger case we also show how
to obtain local energy decay as well as Strichartz-type estimates. For the Airy
equation we obtain a local energy decay that is almost sharp from the scaling
point of view, but nonetheless misses the classical estimates by a gap. This
work is inspired by the work of Klainerman on $L^2$---$L^\infty$ decay of wave
equations, as well as the recent work of Fajman, Joudioux, and Smulevici on
decay of mass distributions for the relativistic Vlasov equation.Comment: 16 pages; expository with some (hopefully) new material. v2: fixed
  typos in the Strichartz exponent, sharpened interpolation to remove epsilon
  loss, updated reference list. v4: added Remark 23 showing how to recover
  standard L^1-L^\infty decay estimates from the weighted L^2-L^\infty argument
  for Schrodinge
Isotropic functions revisited

To a smooth and symmetric function $f$ defined on a symmetric open set
$\Gamma\subset\mathbb{R}^{n}$ and a real $n$-dimensional vector space $V$ we
assign an associated operator function $F$ defined on an open subset
$\Omega\subset\mathcal{L}(V)$ of linear transformations of $V$, such that for
each inner product $g$ on $V$, on the subspace
$\Sigma_{g}(V)\subset\mathcal{L}(V)$ of $g$-selfadjoint operators,
$F_{g}=F_{|\Sigma_{g}(V)}$ is the isotropic function associated to $f$, which
means that $F_{g}(A)=f(\mathrm{EV}(A))$, where $\mathrm{EV}(A)$ denotes the
ordered $n$-tuple of real eigenvalues of $A$. We extend some well known
relations between the derivatives of $f$ and each $F_{g}$ to relations between
$f$ and $F$. By means of an example we show that well known regularity
properties of $F_{g}$ do not carry over to $F$.Comment: 13 pages. Added an example to show that loss of regularity is
  possible. Extended the bibliography. Comments are welcom
Linear systems over localizations of rings

We describe a method for solving linear systems over the localization of a
commutative ring $R$ at a multiplicatively closed subset $S$ that works under
the following hypotheses: the ring $R$ is coherent, i.e., we can compute finite
generating sets of row syzygies of matrices over $R$, and there is an algorithm
that decides for any given finitely generated ideal $I \subseteq R$ the
existence of an element $r$ in $S \cap I$ and in the affirmative case computes
$r$ as a concrete linear combination of the generators of $I$.Comment: Improvement of the metho
Sharp geometric condition for null-controllability of the heat equation
  on $\mathbb{R}^d$ and consistent estimates on the control cost

In this note we study the control problem for the heat equation on
$\mathbb{R}^d$, $d\geq 1$, with control set $\omega\subset\mathbb{R}^d$. We
provide a necessary and sufficient condition (called $(\gamma,
a)$-\emph{thickness}) on $\omega$ such that the heat equation is
null-controllable in any positive time. We give an estimate of the control cost
with explicit dependency on the characteristic geometric parameters of the
control set. Finally, we derive a control cost estimate for the heat equation
on cubes with periodic, Dirichlet, or Neumann boundary conditions, where the
control sets are again assumed to be thick. We show that the control cost
estimate is consistent with the $\mathbb{R}^d$ case.Comment: To appear in Archiv der Mathematik with DOI
  :10.1007/s00013-018-1185-x. A section added with discussion of approximation
  of the control problem on cubes by the control problem on whole Euclidean
  spac
Conley conjecture and local Floer homology

In this paper we connect algebraic properties of the pair-of-pants product in
local Floer homology and Hamiltonian dynamics. We show that for an isolated
periodic orbit the product is non-uniformly nilpotent and use this fact to give
a simple proof of the Conley conjecture for closed manifolds with aspherical
symplectic form. More precisely, we prove that on a closed symplectic manifold
the mean action spectrum of a Hamiltonian diffeomorphism with isolated periodic
orbits is infinite.Comment: 9 pages, revised version, main results unchanged, Archiv der
  Mathematik, 201
A remark on the effect of random singular two-particle interactions

In this note we study a two-particle bound system (molecule) moving on the
positive half-line under the influence of randomly distributed singular
two-particle interactions generated by a Poisson process. We give a rigorous
definition of the underlying Hamiltonian and study its spectral properties. As
a main result we prove that, with finite probability, the random interactions
destroy the discrete part of the spectrum which is present in the free system.
Most interestingly, this phenomenon is somewhat contrary to the role attributed
to random interactions in the context of Anderson localisation where disorder
is generally associated with a suppression of transport
On uniqueness of JSJ decompositions of finitely generated groups

We give an example of two JSJ decompositions of a group that are not related
by conjugation, conjugation of edge-inclusions, and slide moves. This answers
the question of Rips and Sela stated in "Cyclic splittings of finitely
presented groups and the canonical JSJ decomposition," Ann. of Math. 146
(1997), 53-109.
  On the other hand we observe that any two JSJ decompositions of a group are
related by an elementary deformation, and that strongly slide-free JSJ
decompositions are genuinely unique. These results hold for the decompositions
of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu, and also for
accessible decompositions.Comment: 11 pages; shortened and reorganized; mathematical content unchange
The contact zone between the Alcapa and Tisza-Dacia mega-tectonic units of northern Romania in the light of new paleomagnetic data

Paleomagnetic analyses were carried out on samples from 19 localities within two different mega-tectonic units in Northern Romania: Tisza-Dacia (11 localities) and ALCAPA (8 localities). The samples cover a range of different lithologies: (1) Late Cretaceous red-coloured marl to marly limestone, (2) Eo- Oligocene flysch sediments, and (3) mid-Miocene (Langhian) tuffite (Dej tuff and related sediments). The Late Cretaceous and mid-Miocene specimens carry secondary paleomagnetic signals exhibiting a counter clockwise deflection of the paleo-declinations by some 30°, while the Eo-Oligocene localities indicate an overall clockwise deflected (between some 45° and <90°) paleodeclination with respect to present-day north. Clockwise rotation postdates the age of sedimentation (Lower Oligocene), as well as (at least partially) thrusting of the Pienides onto the Tisza-Dacia mega-tectonic unit, which occurred between 20.5 and 18.5 Ma. Clockwise rotation predates post-12 Ma counter clockwise rotations inferred for the mid-Miocene localities. Surprisingly, the clockwise rotations of the first rotational stage not only affected the (par-) autochthonous sedimentary cover of the Tisza-Dacia megatectonic unit, but also the allochthonous flysch nappes of the Pienides, i.e. the eastern tip of the ALCAPA mega-tectonic unit. Well-documented opposed rotation of the remainder of ALCAPA necessitates a detachment of this eastern tip of ALCAPA after 18.5 Ma. The most likely location for this detachment zone is along the margins of the Transcarpathian depression. During a second (post-12 Ma) stage, counter clockwise rotations of up to 30° affected the entire working area. Regarding timing and magnitude, these second stage rotations are similar to rotations documented for the East Slovak basin, but different from those reported from the South Apuseni Mountains and the Central and Inner West Carpathians located west of the East Slovak basin
Latest Pliocene to recent thick-skinned tectonics at the Upper RhineGraben – Jura Mountains junction

The southernmost Upper Rhine Graben and adjacent Jura experienced basement- rooted shortening that occurred after the deposition of the Pliocene fluvial “Sundgau gravels”. Folds affecting the base of these gravels systematically trend NE to ENE. Combined evidence from reflection seismic lines and contour maps of the base-Tertiary and base-Pliocene levels indicates that these folds probably formed by thick-skinned reactivation of both NNE-SSW and WSW-ENE-striking faults. This thick-skinned shortening is NW-SE oriented, i.e. parallel to the maximum horizontal stresses inferred from seismotectonics. NNE-SSW-striking faults (paralleling the Upper Rhine Graben) have been reactivated in sinistral strike-slip mode. However, dextrally transpressive reactivation of the WSW-ENE-trending faults that belong to the Rhine-Bresse Transfer Zone is interpreted to predominate. Deflections of recent river courses around the crests of en-échelon-aligned surface anticlines suggest that the deformation is ongoing at present. Retro-deformation of the folds affecting the base of the Sundgau gravels indicates horizontal displacement rates of about 0.05 mm/a. This corresponds to a minimum strain rate in the order of 2·10-16 s-1, given the maximum time span of 2.9 Ma for this deformation, i.e. the biostratigraphically determined minimum age of the gravels. A change from thin-skinned tectonics, that prevailed during the main phase of Jura folding, to very probably still ongoing thick-skinned tectonics is inferred to have occurred in the Late Pliocene. We speculate that this change might be linked to the incipient inversion of Permo-Carboniferous troughs within the Alpine foreland in general. This inversion in dextrally transpressive or purely compressive mode along a WNW-ESE-trending basement fault, that is part of the Rhine-Bresse Transfer Zone, which in turn was prestructured during the formation of the Permo-Carboniferous troughs, could have triggered the 1356 Basel earthquake
The Alpine-Carpathian-Dinaridic orogenic system : correlation and evolution of tectonic units

A correlation of tectonic units of the Alpine-Carpathian-Dinaridic system of orogens, including the substrate of the Pannonian and Transylvanian basins, is presented in the form of a map. Combined with a series of crustal-scale cross sections this correlation of tectonic units yields a clearer picture of the threedimensional architecture of this system of orogens that owes its considerable complexity to multiple overprinting of earlier by younger deformations. The synthesis advanced here indicates that none of the branches of the Alpine Tethys and Neotethys extended eastward into the Dobrogea Orogen. Instead, the main branch of the Alpine Tethys linked up with the Meliata- Maliac-Vardar branch of the Neotethys into the area of the present-day Inner Dinarides. More easterly and subsidiary branches of the Alpine Tethys separated Tisza completely, and Dacia partially, from the European continent. Remnants of the Triassic parts of Neotethys (Meliata-Maliac) are preserved only as ophiolitic mélanges present below obducted Jurassic Neotethyan (Vardar) ophiolites. The opening of the Alpine Tethys was largely contemporaneous with the Latest Jurassic to Early Cretaceous obduction of parts of the Jurassic Vardar ophiolites. Closure of the Meliata-Maliac Ocean in the Alps and West Carpathians led to Cretaceous-age orogeny associated with an eclogitic overprint of the adjacent continental margin. The Triassic Meliata- Maliac and Jurassic Western and Eastern Vardar ophiolites were derived from one single branch of Neotethys: the Meliata-Maliac-Vardar Ocean. Complex geometries resulting from out-of-sequence thrusting during Cretaceous and Cenozoic orogenic phases underlay a variety of multi-ocean hypotheses, that were advanced in the literature and that we regard as incompatible with the field evidence. The present-day configuration of tectonic units suggests that a former connection between ophiolitic units in West Carpathians and Dinarides was disrupted by substantial Miocene-age dislocations along the Mid-Hungarian Fault Zone, hiding a former lateral change in subduction polarity between West Carpathians and Dinarides. The SW-facing Dinaridic Orogen, mainly structured in Cretaceous and Palaeogene times, was juxtaposed with the Tisza and Dacia Mega-Units along a NW-dipping suture (Sava Zone) in latest Cretaceous to Palaeogene times. The Dacia Mega-Unit (East and South Carpathian Orogen, including the Carpatho-Balkan Orogen and the Biharia nappe system of the Apuseni Mountains), was essentially consolidated by E-facing nappe stacking during an Early Cretaceous orogeny, while the adjacent Tisza Mega-Unit formed by NW-directed thrusting (in present-day coordinates) in Late Cretaceous times. The polyphase and multi-directional Cretaceous to Neogene deformation history of the Dinarides was preceded by the obduction of Vardar ophiolites onto to the Adriatic margin (Western Vardar Ophiolitic Unit) and parts of the European margin (Eastern Vardar Ophiolitic Unit) during Late Jurassic to Early Cretaceous times
Ammonoids of the Middle/Late Anisian boundary (Middle Triassic) and the transgression of the Prezzo Limestone in eastern Lombardy-Giudicarie (Italy)

This study documents ammonoids with a precise stratigraphic control at the middle/late Anisian (Pelsonian/Illyrian) boundary from a new locality in eastern Lombardy-Giudicarie (Monte Guglielmo) and from classical sections in Giudicarie. These ammonoid faunas allow revising the taxonomic interpretation of Ceratites cimeganus Mojsisovics 1882 and of the genus Paraceratites Hyatt 1900. Ceratites cimeganus is here assigned to the North American genus Rieppelites Monnet & Bucher 2005. In eastern Lombardy-Giudicarie, R. cimeganus is diagnostic of a distinct biochronological unit (cimeganus Zone) bracketed between the older Bulogites zoldianus Zone and the younger Judicarites euryomphalus–Paraceratites trinodosus zones. The recognition of this cimeganus Zone significantly improves worldwide correlation since it is recognized in several other Tethyan basins (Dolomites, Northern Calcareous Alps) as well as in North America (Nevada). These new data allow a redefinition of the middle/late Anisian boundary in the western Tethys, which is here intercalated between the zoldianus and cimeganus zones. This limit is marked by a clear ammonoid turnover (e.g. disappearance of  Acrochordiceras and Balatonites, appearance of Rieppelites). Finally, the presence of sections including the cimeganus Zone in eastern Lombardy-Giudicarie allow the establishment of local gaps in sedimentation, which may reflect the regional and important transgression of the pelagic Prezzo Limestone over the shallow water platform carbonates of a “Camorelli-Dosso dei Morti barrier”, as also underlined by the spatial distribution of brachiopod lumachellas