segre product of artin schelter regular algebras of dimension 2 and embeddings in quantum p3 s the segre embedding of p1 p1as a smooth quadricqin p3corresponds to the surjection of the four dimensional polynomial ring onto the segre productsof two copies of the homogeneous coordinate ring of p1 we study segre products of noncommutative algebras if in particularaandbare two copies of a quantum p1thens i ai kbi is a twisted homogeneous coordinate ring of the quadricq the main result of this paper is the classification of all embeddings of the segre product of two quantum planes into so called quantum p3 s these are the proj of artin schelter regular algebrasrof global dimension four with the hilbert series of a commutative polynomial ring and which map ontos ifris not a twist of a polynomial ring then the point scheme ofreither is the union of the quadricqwith a line or is only the quadricq in the first case ris a central extension of a three dimensional artin schelter regular algebra and a twist of an algebra mapping onto the commutative homogeneous coordinate ring ofq in the second case such an algebraris the first known example of a four dimensional artin schelter regular algebra which is not determined by its point scheme

analysis on besov spaces ii embedding and duality theorems abstract this paper gives several results on besov spaces of holomorphic functions on a very large class of domains d in c n they include duality theorem embedding theorem best growth estimate and boundedness of multiplication operators on besov spaces

modules of finite projective dimension with negative intersection multiplicities let x be the image of x in r the main object of this paper is to study modules of finite length and finite projective dimension over r one consequence of our study will be counterexamples to several conjectures concerning the behavior of intersection multiplicities for modules of finite projective dimension let denote length if s is a noetherian ring m n are finitely generated s modules l m is finite and d pdsm we may define following serre is d zs m n z m n 1 tors m n

intersection multiplicity of serre on regular schemes abstract the study of the intersection multiplicity function o x f g over a regular scheme x for a pair of coherent o x modules f and g is the main focus of this paper we mostly concentrate on projective schemes vector bundles over projective schemes regular local rings and their blow ups at the closed point we prove that a vanishing holds in all the above cases b positivity holds over proj of a graded ring finitely generated over its 0th component which is artinian local when one of f and g has a finite resolution by direct sum of copies of o t for various t and c non negativity holds over p r n r regular local and over arbitrary smooth projective varieties if their tangent bundles are generated by global sections we establish a local global relation for for a pair of modules over a regular local ring via of their corresponding tangent cones and of their corresponding blow ups a new proof of vanishing and a special case of positivity for serre s conjecture are also derived via this approach we also demonstrate that the study of non negativity is much more complicated over blow ups particularly in the mixed characteristics

complexity and tor on a complete intersection let r m be a complete intersection that is a local ring whose m adic completion is the quotient of a regular local ring by a regular sequence supposemis a finitely generatedr module it is known that the even and odd betti sequences ofmare eventually given by polynomials of the same degreen the complexity ofmis the nonnegative integern 1 we use this notion of complexity to study the vanishing of torri m n for finitely generated modulesmandnover a complete intersectionr we prove several theorems dealing with rigidity of tor which are generalizations and in certain situations improvements of known results the main idea of these rigidity theorems is that the number of consecutive vanishing tors required in the hypothesis of a rigidity theorem depends more on the minimum of the complexities ofmandnrather than on the codimension ofr we give examples showing that this dependence is sharp we also show that ifm rnhas finite length then for sufficiently high indices two consecutive vanishing tors force the vanishing of all higher tors

multipliers of mobius invariant qs spaces the spaceqs 0 s consists of those f which are analytic in the unit disc mathbb d and such that sup a in mathbb d int limits mathbb d f z 2 1 varphi a z 2 s da z infty where varphi a z frac a z 1 overline a z we give a complete description of m qs the algebra of pointwise multipliers of qs by proving xiao s conjecture which says that f m qs if and only if f h and sup a in mathbb d left rm log frac 2 1 a right 2 int limits mathbb d f z 2 1 varphi a z 2 s da z infty

intersection multiplicity over noncommutative algebras abstract in this paper we will prove serre s multiplicity conjectures for large class of connected algebras not necessarily commutative using the intersection multiplicity defined by ext groups instead of tor groups since this new definition of the intersection multiplicity agrees with classical serre s definition for nice commutative rings the result is a noncommutative version of that of peskine and szpiro the result also applies to noncommutative filtered algebras in certain situations

inverse curvature flows in asymptotically robertson walker spaces abstract in this paper we consider inverse curvature flows in a lorentzian manifold n which is the topological product of the real numbers with a closed riemannian manifold and equipped with a lorentzian metric having a future singularity so that n is asymptotically robertson walker the flow speeds are future directed and given by 1 f where f is a homogeneous degree one curvature function of class k of the principal curvatures i e the n th root of the gauss curvature we prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric

on negativity of higher euler characteristics positivity of higher euler characteristics on equicharacteristic and unramified regular local rings follow from the works of serre lichtenbaum and hochster here we prove that such higher euler characteristics could be negative on complete intersections even for a pair of intersecting modules both having finite projective dimension satisfying serre vanishing

the inverse mean curvature flow in warped cylinders of non positive radial curvature abstract we consider the inverse mean curvature flow in smooth riemannian manifolds of the form r 0 s n g with metric g d r 2 2 r and non positive radial sectional curvature we prove that for initial mean convex graphs over s n the flow exists for all times and remains a graph over s n under weak further assumptions on the ambient manifold we prove optimal decay of the gradient and that the flow leaves become umbilic exponentially fast we prove optimal c 2 estimates in case that the ambient pinching improves

connected graded gorenstein algebras with enough normal elements we generalize 12 1 1 and 1 2 to the following situation theorem 1 let a be a connected graded noetherian algebra of injective dimension d such that every nonsimple graded prime factor ring of a contains a homogeneous normal element of positive degree then 1 a is auslander gorenstein and cohen macaulay 2 a has a quasi frobenius quotient ring 3 every minimal prime ideal p is graded andgkdim a p d 4 if moreover a has finite global dimension then a is a domain and a maximal order in its quotient division ring to prove the above we need the following result which is a generalization of 3 2 46 ii theorem 2 let a be a connected graded noetherian as gorenstein algebra of injective dimension d then 1 the last term of the minimal injective resolution of aais isomorphic to a shift of a 2 for every noetherian graded a module m extd m a is finite dimensional over k

homological properties of balanced cohen macaulay algebras a balanced cohen macaulay algebra is a connected algebra a having a balanced dualizing complex a d in the sense of yekutieli 1992 for some integer d and some graded a a bimodule a we study some homological properties of a balanced cohen macaulay algebra in particular we will prove the following theorem theorem 0 1 let a be a noetherian balanced cohen macaulay algebra and m a nonzero finitely generated graded left a module then 1 m has a finite resolution of the form 0 a l mj a l 1j h m 0 where h is a finitely generated maximal cohen macaulay graded left a module 2 m has finite injective dimension if and only if m has a finite resolution of the form 0 a l mj a l 1j a l 0j m 0 as a corollary we will have the following characterizations of as gorenstein algebras and as regular algebras corollary 0 2 let a be a noetherian balanced cohen macaulay algebra 1 a is as gorenstein if and only if a has finite projective dimension as a graded left a module 2 a is as regular if and only if every finitely generated maximal cohen macaulay graded left a module is free

inverse anisotropic mean curvature flow and a minkowski type inequality abstract in this paper we show that the inverse anisotropic mean curvature flow in r n 1 initiating from a star shaped strictly f mean convex hypersurface exists for all time and after rescaling the flow converges exponentially fast to a rescaled wulff shape in the c topology as an application we prove a minkowski type inequality for star shaped f mean convex hypersurfaces

pointwise multipliers and decomposition theorems in analytic besov spaces for the holomorphic besov spaces mathcal b p s in the unit ball of mathbb c n we study necessary and sufficient conditions on holomorphic functions g 1 g 2 so that the operator f 1 f 2 mapsto g 1f 1 g 2f 2 maps mathcal b p s times mathcal b p s onto mathcal b p s related to this problem we also obtain some characterizations of the pointwise multipliers for these spaces

on maps of grothendieck groups induced by completion abstract we prove that the induced map g 0 a g 0 a by completion is injective if a is an excellent noetherian local ring that satisfies one of the following three conditions i a is henselian ii a is a local ring at the homogeneous maximal ideal of a homogeneous ring over a field iii a has at most isolated singularity

bmo in the bergman metric on bounded symmetric domains for bounded symmetric domains in cn a notion of bounded mean oscillation in terms of the bergman metric is introduced it is shown that for in l2 dv is in bmo if and only if the densely defined operator m p m p pm on l2 dv is bounded here m is multiplication by and p is the bergman projection with range the bergman subspace h2 dv la2 dv of holomorphic functions in l2 dv an analogous characterization of compactness for m p is provided by functions of vanishing mean oscillation at the boundary of

inverse curvature flows in riemannian warped products abstract the long time existence and umbilicity estimates for compact graphical solutions to expanding curvature flows are deduced in riemannian warped products of a real interval with a compact fibre notably we do not assume the ambient manifold to be rotationally symmetric nor the radial curvature to converge nor a lower bound on the ambient sectional curvature the inverse speeds are given by powers 0 p 1 of a curvature function satisfying few common properties

divergent series and serre s intersection formula for graded rings abstract on a smooth variety serre s intersection formula computes intersection multiplicities via an alternating sum of the lengths of tor groups when the variety is singular the corresponding sum can be a divergent series but there are alternate geometric approaches for assigning often fractional intersection multiplicities in some singular settings our motivating question comes from fulton who asks whether an analytic continuation of the divergent series from serre s formula can be related to these fractional multiplicities we apply work of avramov and buchweitz to answer fulton s question in the context of graded rings

quasilength latent regular sequences and content of local cohomology abstract the quasilength of a finitely generated module that is killed by a power of a finitely generated ideal i is introduced it is the length of a shortest filtration of the module with factors that are cyclic modules killed by i this notion is then used to define a notion of content for the dth local cohomology module of a ring or module with support in an ideal generated by d elements in the case of a ring which is central this content is a real number between 0 and 1 it is not known whether it is independent of the choice of the d generators nor whether it can change if the generators are replaced by powers in positive prime characteristic it is shown that the content is always 0 or 1 this is an open question in equal characteristic 0 and in mixed characteristic it is conjectured that if the elements form a system of parameters in a local ring of dimension d then the content is 1 this is proved if the ring contains a field in mixed characteristic it is an open question in dimension 3 or more and implies the direct summand conjecture the relationship between the notions of quasilength and content and the property that a sequence of elements can become a regular sequence on a ring or module after base change is explored

the pointwise multipliers of bloch type space βp and dirichlet type space dq on the unit ball of cn abstract in the paper we will discuss the pointwise multipliers from dirichlet type space d p to bloch type space q on the unit ball of c n the multiplier spaces m d p q are fully characterized for all p q

intersection multiplicities over gorenstein rings let r be a complete local ring of dimension d over a perfect field of prime characteristic p and let m be an r module of finite length and finite projective dimension s dutta showed that the equality lim n to infty frac ell f n r m p nd ell m holds when the ring r is a complete intersection or a gorenstein ring of dimension at most 3 we construct a module over a gorenstein ring r of dimension five for which this equality fails to hold this then provides an example of a nonzero todd class tau 3 r and of a bounded free complex whose local chern character does not vanish on this class

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

intersection multiplicity of modules in the positive characteristics abstract we introduce an asymptotic length criteria on tor 0 and tor 1 of a pair of modules via the frobenius map to study positivity and non negativity of serre intersection multiplicity over local complete intersections and gorenstein rings in the positive characteristics when both modules have finite projective dimension we use this criteria to derive a sufficient condition for a non negativity over complete intersections when one of the modules has dimension 2 and b non negativity over gorenstein rings of dimension 5 we also show that the problem of intersection multiplicity on local rings complete intersection gorenstein cohen macaulay in characteristic 0 can be reduced to local rings complete intersection gorenstein cohen macaulay respectively in the positive characteristics

integral type operators from iterated logarithmic bloch spaces to zygmund type spaces let h b denote the space of all holomorphic functions on the unit ball b of c n and rh z j 1 nz j h z j z the radial derivative of h in this paper we study the boundedness and compactness of the following integral operator t g f z 0 1f tz rg tz dtt f h b z b from iterated logarithmic bloch spaces to zygmund type spaces

function theory on cartan domains and the berezin toeplitz symbol calculus cn with dv z normalized lebesgue measure on 9 we let l l2 q dv be the usual space of lebesgue square integrable complex valued functions on 9 by h2 h2 q dv we denote the bergman subspace of l2 consisting of holomorphic functions the orthogonal projection operator from l2 onto h2 is denoted by p forf in l q the space of essentially bounded measurable functions on 9 we will consider the multiplication operator

isoperimetric type problems and alexandrov fenchel type inequalities in the hyperbolic space abstract in this paper we solve various isoperimetric problems for the quermassintegrals and the curvature integrals in the hyperbolic space h n by using quermassintegral preserving curvature flows as a byproduct we obtain hyperbolic alexandrov fenchel inequalities

the inverse mean curvature flow perpendicular to the sphere we consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in mathbb r n 1 which are perpendicular to the unit sphere from the inside we prove that the flow hypersurfaces converge to the embedding of a flat disk in the norm of c 1 beta beta 1

inscribed radius estimates for inverse curvature flow in sphere and hyperbolic space abstract in this paper we study a fully nonlinear inverse curvature flow in sphere and hyperbolic space and prove a non collapsing property for this flow using maximum principle precisely when ambient space is sphere we show that upon some conditions on speed function the radius of the largest touching interior ball is bounded below by a multiple of the reciprocal of the speed where ambient space is hyperbolic we obtain an upper bound of the curvature of the largest touching interior ball for star shaped inverse mean curvature flow

on an integral type operator from iterated logarithmic bloch spaces into bloch type spaces let h b denote the space of all holomorphic functions on the open unit ball b of c n let f f 1 f n be a holomorphic self map of b and email protected h b such that g 0 0 in this paper we study the boundedness and compactness of the following integral type operator recently introduced by xiangling zhu and the second authori f gf z email protected 0 1rf f tz g tz dtt email protected b from the iterated logarithmic bloch spaces into the bloch type spaces for the case when f z z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic bloch space into the little bloch type space

tensor products of modules and the rigidity of tor let r be a hypersurface domain that is a ring of the form s f where s is a regular local ring and f is a prime element suppose m and n are finitely generated r modules we prove two rigidity theorems on the vanishing of tor in the first theorem we assume that the regular local ring s is unramified that m r n has finite length and that dim m dim n dim r with these assumptions if tor r m n 0 for some j 0 then tor r m n 0 for all i j the second rigidity theorem states that if m r n is reflexive then tor r m n 0 for all i 1 we use these theorems to prove the following theorem valid even if s is ramified if m r n is a maximal cohen macaulay r module then both m and n are maximal cohen macaulay modules and at least one of them is free

pointwise multipliers and decomposition theorems in f q s in this paper we give a characterization of the pointwise multipliers of the holomorphic triebel lizorkin spaces f q s and we apply these results to prove a corona decomposition theorem for these spaces

a minkowski inequality for hypersurfaces in the anti de sitter schwarzschild manifold we prove a sharp inequality for hypersurfaces in the n dimensional anti de sitter schwarzschild manifold for general n 3 this inequality generalizes the classical minkowski inequality for surfaces in the three dimensional euclidean space and has a natural interpretation in terms of the penrose inequality for collapsing null shells of dust the proof relies on a new monotonicity formula for inverse mean curvature flow and uses a geometric inequality established by the first author in 3 c 2015 wiley periodicals inc

stability of the pmt and rpi for asymptotically hyperbolic manifolds foliated by imcf we study the stability of the positive mass theorem and the riemannian penrose inequality in the case where a region of an asymptotically hyperbolic manifold m3 can be foliated by a smooth solution of inverse mean curvature flow imcf which is uniformly controlled we consider a sequence of regions of asymptotically hyperbolic manifolds uti mi3 foliated by a smooth solution to imcf which is uniformly controlled and if uti 0i ti and mh ti 0 then uti converges to a topological annulus portion of the hyperbolic space with respect to l2 metric convergence if instead mh ti mh 0i 0 and mh ti m 0 then we show that uti converges to a topological annulus portion of the anti de sitter schwarzschild metric with respect to l2 metric convergence

test modules to calculate dutta multiplicities using frobenius maps the dutta multiplicity f was first defined by dutta for a complex f over a local ring of positive characteristic nowadays using localized chern characters or adams operations it is defined for a complex not only over a local ring of positive characteristic but also over a ring that is a homomorphic image of an arbitrary regular local ring in the paper we shall give another characterization to dutta multiplicity using some galois extension furthermore we shall define the notion of test modules if a test module for a local ring exists then the positivity conjecture of dutta multiplicities is true over the ring in the paper it is proved that if the small cohen macaulay modules conjecture is true then test modules always exist for complete local domains whose field of fractions are of characteristic 0

harmonic mean curvature flow and geometric inequalities abstract we employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in hyperbolic space to prove alexandrov fenchel type inequalities relating quermassintegrals to the total curvature which is the integral of gaussian curvature on the hypersurface the resulting inequality allows us to use the inverse mean curvature flow to prove alexandrov fenchel inequalities between the total curvature and the area for strictly convex hypersurfaces finally we apply the harmonic mean curvature flow to prove a new class of geometric inequalities for h convex hypersurfaces in hyperbolic space

toeplitz operators on bloch type spaces in the unit ball of cn abstract for 1 2 we consider the toeplitz operator t on bloch type space b b n in the unit ball of c n where is a positive borel measure on b n we give the necessary and sufficient conditions for t to be bounded or compact on b b n therefore positive borel measure on b n is completely characterized for which t is bounded or compact on the bloch type space b b n

symmetry in the vanishing of ext over stably symmetric algebras abstract a frobenius algebra over a field k is called symmetric if the nakayama automorphism is an inner automorphism a stably symmetric algebra is defined to be a generalization of a symmetric k algebra in this paper we will study symmetry in the vanishing of ext for such algebras r namely for all finitely generated r modules m and n ext r i m n 0 for all i 0 if and only if ext r i n m 0 for all i 0 we show that a certain class of noetherian stably symmetric gorenstein algebras such as the group algebra of a finite group and the exterior algebra k n when n is odd have this symmetry using serre duality we also show that every exterior algebra k n whether n is even or odd has this symmetry for graded modules using koszul duality

the qp carleson measure problem let be a nonnegative borel measure on the open unit disk this note shows how to decide that the mobius invariant space covering and is boundedly resp compactly embedded in the quadratic tent type space interestingly the embedding result can be used to determine the boundedness resp compactness of the volterra type and multiplication operators on

a penrose type inequality for graphs over reissner nordstrom anti desitter manifold in this paper we use the inverse mean curvature flow to establish an optimal minkowski type inequality a weighted alexandrov fenchel inequality for the mean convex star shaped hypersurfaces in the reissner nordstrom anti desitter manifold and a penrose type inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over the reissner nordstrom anti desitter manifold

new estimates of essential norms of weighted composition operators between bloch type spaces abstract we give estimates of the essential norms of the weighted composition operators u c between different bloch type spaces in terms of the n th power of we also give similar characterizations for boundedness and compactness of u c between different bloch type spaces

locally constrained curvature flows and geometric inequalities in hyperbolic space in this paper we first study the locally constrained curvature flow of hypersurfaces in hyperbolic space which was introduced by brendle guan and li an inverse curvature type hypersurface flow in mathbb h n 1 preprint this flow preserves the mth quermassintegral and decreases m 1 th quermassintegral so the convergence of the flow yields sharp alexandrov fenchel type inequalities in hyperbolic space some special cases have been studied in brendle et al in the first part of this paper we show that h convexity of the hypersurface is preserved along the flow and then the smooth convergence of the flow for h convex hypersurfaces follows we then apply this result to establish some new sharp geometric inequalities comparing the integral of kth gauss bonnet curvature of a smooth h convex hypersurface to its mth quermassintegral for 0 le m le 2k 1 le n and comparing the weighted integral of kth mean curvature to its mth quermassintegral for 0 le m le k le n in particular we give an affirmative answer to a conjecture proposed by ge wang and wu math z 281 257 297 2015 in the second part of this paper we introduce a new locally constrained curvature flow using the shifted principal curvatures this is natural in the context of h convexity we prove the smooth convergence to a geodesic sphere of the flow for h convex hypersurfaces and provide a new proof of the geometric inequalities proved by andrews chen and the third author of this paper in 2018 we also prove a family of new sharp inequalities involving the weighted integral of kth shifted mean curvature for h convex hypersurfaces which as application implies a higher order analogue of brendle hung and wang s commun pure appl math 69 1 124 144 2016 inequality

multiplicities and a dimension inequality for unmixed modules abstract we prove the following result which is motivated by the recent work of kurano and roberts on serre s positivity conjecture assume that r m is a local ring with finitely generated module m such that r ann m is quasi unmixed and contains a field and that p and q are prime ideals in the support of m such that p is analytically unramified p q m and e m p e m then dim r p dim r q dim m we also prove a similar theorem in a special case of mixed characteristic finally we provide several examples to explain our assumptions as well as an example of a noncatenary local domain r with prime ideal p such that e rp e r 1

pointwise multipliers from dirichlet type spaces dτ to qp spaces in the unit ball of cn abstract in this paper the pointwise multipliers m d q p and m d q p 0 are characterized in the unit ball of c n for the values of p in the three cases i n n 1 n p 1 ii n n 1 n p 1 and iii n n 1 n p 1 in particular the multiplier spaces m d bmoa and m d vmoa are discussed correspondingly for all and the sharp embeddings of m d n bmoa and m d n vmoa in bloch spaces are shown respectively

the gbc mass for asymptotically hyperbolic manifolds the paper consists of two parts in the first part by using the gauss bonnet curvature which is a natural generalization of the scalar curvature we introduce a higher order mass the gauss bonnet chern mass m mathbb h k for asymptotically hyperbolic manifolds and show that it is a geometric invariant moreover we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs and establish a relationship between the corresponding penrose type inequality for this mass and weighted alexandrov fenchel inequalities in the hyperbolic space mathbb h n in the second part we establish these weighted alexandrov fenchel inequalities in mathbb h n for any horospherical convex hypersurface sigma begin aligned int sigma v sigma 2k 1 d mu ge c n 1 2k 1 omega n 1 left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned where sigma j is the j th mean curvature of sigma subset mathbb h n v cosh r and sigma is the area of sigma as an application we obtain an optimal penrose type inequality for the new mass defined in the first part begin aligned m k mathbb h ge frac 1 2 k left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned for asymptotically hyperbolic graphs with a horizon type boundary sigma provided that a dominant energy type condition tilde l k ge 0 holds both inequalities are optimal

the dynamics of leavitt path algebras abstract recently it was shown that the notion of flow equivalence of shifts of finite type in symbolic dynamics is related to the morita theory and the grothendieck group in the theory of leavitt path algebras abrams et al 2011 4 in this paper we show that the notion of the conjugacy of shifts of finite type is closely related to the graded morita theory and consequently the graded grothendieck group this fits into the general framework we have in these two theories conjugacy yields the flow equivalence and the graded morita equivalence can be lifted to the morita equivalence starting from a finite directed graph the observation that the graded grothendieck group of the leavitt path algebra associated to e coincides with the krieger dimension group of the shift of finite type associated to e provides a link between the theory of leavitt path algebras and symbolic dynamics it has been conjectured that the ordered graded grothendieck group as z x x 1 module we call this the graded dimension group classifies the unital leavitt path algebras completely hazrat 2013 20 via the above correspondence utilising the results from symbolic dynamics we prove that for two purely infinite simple unital leavitt path algebras if their graded dimension groups are isomorphic then the algebras are isomorphic

bmo on strongly pseudoconvex domains hankel operators duality and overline partial estimates we study the condition that characterizes the symbols of bounded hankel operators on the bergman space of a strongly pseudoconvex domain and show that it is equivalent to bmo plus analytic here we mean the bergman metric bmo of berger coburn and zhu in the course of the proof we obtain new 0 estimates that may be of independent interest some applications include a decomposition of bmo similar to the classical li l and two characterizations of the dual of vmo which is also a predual of bmo in addition we obtain some partial results on the boundedness of hankel operators in l1 norm

lengths of tors determined by killing powers of ideals in a local ring given a local ring r and n ideals whose sum is primary to the maximal ideal of r one may define a function which takes an n tuple of exponents a1 an to the length of tork r i1 r in these functions are shown to have rational generating functions in certain cases

constructing modules of finite projective dimension with prescribed intersection multiplicities abstract recently roberts and srinivas proved the existence of large classes of modules of finite length and finite projective dimension with prescribed intersection multiplicities giving many new counterexamples to earlier vanishing conjectures we present an explicit method for constructing the examples whose existence is implied by their theorem

the multipliers between the mixed norm spaces in cn abstract in this paper we discuss the pointwise multipliers between the mixed norm spaces on the unit ball of c n for normal functions 1 and 2 we give several full characterizations of the pointwise multipliers m h p q 1 h p q 2 for 0 p 0 q and m h p p 1 h q q 2 for 0 p 0 q

a new proof of the new intersection theorem abstract in 1987 roberts completed the proof of the new intersection theorem nit by settling the mixed characteristic case using local chern characters as developed by fulton and also by roberts his proof has been the only one recorded of the nit in mixed characteristic this paper gives a new proof of this theorem one which mostly parallels roberts original proof but avoids the use of local chern characters instead the proof here uses adams operations on k theory with supports as developed by gillet and soule

laurent coefficients and ext of finite graded modules n m the present investigation started as an attempt to explain this intriguing formula and to nd out whether analogous equalities exist for subsequent coe cients of laurentexpansions around 1 fairly complete answers are presented in sections 3 and 4 theydepend on embedding 1 into an equality of laurent series which predicts an in nitesequence of similar relations among higher laurent coe cients the results are proved insection 1 and are used in section 2 to obtain non trivial lower bounds for the bass numbersof certain graded modules of nite injective dimension

diagonalizing the frobenius abstract over a noetherian local ring r of prime characteristic p the frobenius functor f r induces a diagonalizable map on certain quotients of rational grothendieck groups this leads to an explicit formula for the dutta multiplicity and it is shown that a weaker version of serre s vanishing conjecture holds whenever f r x p dim r x for all bounded complexes x of finitely generated projective modules with finite length homology

bounded and compact operators on the bergman space la1 in the unit ball of cn abstract let be a complex borel measure on the unit ball of c n and 1 we characterize the measures for which the toeplitz operator t is bounded or compact on the bergman space l a 1 b n 1 z 2 d where d is the normalized lebesgue measure on the unit ball of c n our results also include the case of more general operators in l a 1 b n d these results extend to several dimensions the results of agbor bekolle and tchoundja 2011 2 and wu zhao and zorborska 2006 11

duality and hankel operators on the bergman spaces of bounded symmetric domains soit un domaine symetrique borne dans c n avec dv la mesure de volume normalisee l espace de bergman l a p est le sous espace clos de l p dv constitue des fonctions holomorphes on decrit le dual et le predual de l a 1 pour tous les domaines symetriques bornes

numerical equivalence defined on chow groups of noetherian local rings in the present paper we define a notion of numerical equivalence on chow groups or grothendieck groups of noetherian local rings which is an analogue of that on smooth projective varieties under a mild condition it is proved that the chow group modulo numerical equivalence is a finite dimensional vector space as in the case of smooth projective varieties numerical equivalence on local rings is deeply related to that on smooth projective varieties for example if grothendieck s standard conjectures are true then a vanishing of chow group of local rings modulo numerical equivalence can be proven using the theory of numerical equivalence the notion of numerically roberts rings is defined it is proved that a cohen macaulay local ring of positive characteristic is a numerically roberts ring if and only if the hilbert kunz multiplicity of a maximal primary ideal of finite projective dimension is always equal to its colength numerically roberts rings satisfy the vanishing property of intersection multiplicities we shall prove another special case of the vanishing of intersection multiplicities using a vanishing of localized chern characters

intersection multiplicity of serre in the unramified case abstract we describe here some recent progress pertaining to the serre intersection multiplicity conjecture in particular we show that if a is unramified then just as in the equicharacteristic case the intersection multiplicity of two modules is bounded below by the product of their hilbert samuel multiplicities we also explain in terms of the blowup of spec a the geometric significance of achieving this lower bound

a dimension inequality for cohen macaulay rings the recent work of kurano and roberts on serre s positivity conjecture suggests the following dimension inequality for prime ideals p and q in a local cohen macaulay ring a n such that e ap e a we have dim a p dim a q dim a we establish this dimension inequality for excellent local cohen macaulay rings which contain a field for certain low dimensional cases and when r p is regular

a geometric inequality on hypersurface in hyperbolic space in this paper we use the inverse curvature flow to prove a sharp geometric inequality on star shaped and two convex hypersurface in hyperbolic space

asymmetry of ext groups in this paper we will use techniques of noncommutative projective geometry to construct examples of algebras r over a field k not satisfying the following two types of symmetric behaviors of ext groups ee for any pair of finitely generated r modules m n dimkextri m n for all i n if and only if dimkextri n m for all i n ee for any pair of finitely generated r modules m n extri m n 0 for all i 0 if and only if extri n m 0 for all i 0 in particular and contrary to the commutative case we give a simple example of a noncommutative noetherian gorenstein frobenius local algebra satisfying uac uniform auslander condition but not satisfying ee

a counterexample to the rigidity conjecture for rings an example is constructed of a local ring and a module of finite type and finite projective dimension over that ring such that the module is not rigid this shows that the rigidity conjecture is false

products of composition multiplication and radial derivative operators from logarithmic bloch spaces to weighted type spaces on the unit ball abstract let h b denote the space of all holomorphic functions on the unit ball b of c n h b and be a holomorphic self map of b let c m and r denote the composition multiplication and radial derivative operators respectively in this paper we characterize the boundedness and compactness of linear operators induced by products of these operators from logarithmic bloch spaces to weighted type spaces on the unit ball