on the gauss algebra associated to a rational map pd pn abstract letkbe a field of characteristic zero given a polynomial ringboverkand a finitely generatedk subalgebraa b one associates toaak subalgebra g a bin such a way that whenais generated byn 1 forms of the same degree then so is g a and moreover in this case g a is the homogeneous coordinate ring of the gauss image of proj a p nin the plucker embedding of the grassmannian g d n whered dim proj a the precise structure of g a is established whenais the homogeneous coordinate ring of a veronese embedding of p dor of a projective monomial curve

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

from geometric quantization to moyal quantization it is shown how the moyal product of phase space functions and the weyl correspondence between symbols and operator kernels may be obtained directly using the procedures of geometric quantization applied to the symplectic groupoid constructed by doubling the phase space

quadratic variation of martingales in riesz spaces national research foundation of south africa grant specific unique reference number uid 85672 and by gnampa of italy u 2012 000574 20 07 2012 and u 2012 000388 09 05 2012

on birational macaulayfications and cohen macaulay canonical modules abstract the aim of the paper is twofold at first there is a characterization of those local domains admitting a birational macaulayfication it turns out that a local domain a quotient of a gorenstein ring possesses a cohen macaulay birational extension b if and only if its canonical module k a is a cohen macaulay module in this situation it follows that b is isomorphic to the endomorphism ring of k a the second part of the paper is devoted to the question when the canonical module of a local ring is a cohen macaulay module there are applications on sequentially cohen macaulay rings a large class of rings whose canonical module are cohen macaulay is given by the simplicial affine semigroup rings as a technical tool there is a spectral sequence related to the duality with respect to the dualizing complex

unbounded order convergence and application to martingales without probability abstract a net x in a vector lattice x is unbounded order convergent uo convergent to x if x x y o 0 for each y x and is unbounded order cauchy uo cauchy if the net x x is uo convergent to 0 in the first part of this article we study uo convergent and uo cauchy nets in banach lattices and use them to characterize banach lattices with the positive schur property and kb spaces in the second part we use the concept of uo cauchy sequences to extend doob s submartingale convergence theorems to a measure free setting our results imply in particular that every norm bounded submartingale in l 1 f is almost surely uo cauchy in f where f is an order continuous banach lattice with a weak unit

links of prime ideals and their rees algebras abstract in a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in gorenstein rings are equimultiple ideals with reduction number 1 this led to the construction of large families of cohen macaulay rees algebras the first goal of this paper is to extend this result to arbitrary cohen macaulay rings the means of the proof are changed since one cannot depend so heavily on linkage theory we then study the structure of the rees algebra of these links more specifically we describe their canonical module in sufficient detail to be able to characterize self linked prime ideals in the last section multiplicity estimates for classes of such ideals are established

geometric quantization of the brst charge in the first half of this paper sects 1 4 we generalise the standard geometric quantization procedure to symplectic supermanifolds in the second half sects 5 6 we apply this to two examples that exhibit classical brst symmetry i e we quantize the brst charge and the ghost number more precisely in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with ad equivariant moment map in the second example we consider a foliated configuration space whose cotangent bundle admits the construction of a brst charge associated to this foliation we show that the classical brst symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space and that geometric quantization gives us a super unitary representation of this supergroup finally we point out how these results are related to reduction at the quantum level as compared with the reduction at the classical level

completeness for vector lattices abstract a net x in a vector lattice x is unbounded order convergent uo convergent to x if x x y is order convergent to 0 for each y x and is unbounded order cauchy uo cauchy if the net x x is unbounded order convergent to 0 the vector space x is unbounded order complete uo complete if every uo cauchy net in x is uo convergent recently li and chen proved that a vector lattice having the countable sup property is universally complete if it is uo complete the main result of this paper states that this equivalence is still true without any further assumption on the vector lattice x which answers an open question asked by li and chen some applications to this are given too

birational extensions in dimension two and integrally closed ideals the aim of this paper is to examine primarily from an algebraic point of view the structure of a 2 dimensional normal local domain s n which birationally dominates a 2 dimensinal regular local ring r m from the geometric point of view the sine qua non is lipman s paper lr on rational singularities for it follows from one of the early results in that paper that s has a rational singularity using elementary algebraic techniques we are able to recover much information concerning the structure of s we have particularly focused on the fact from lipman ll and artin ar that s must have minimal multiplicity we hope this approach will aid in understanding the algebra of rational singularities and in the exploration of many open questions in dimension two and in higher dimensions the framework of the paper is set up as follows in the first section we use basic algebraic techniques such as analytic independence and zariski s main theorem to prove for example that s has a regular height 1 prime if r m is infinite if s is not regular we may assume that r is maximally regular in s and when this is the case we show for instance that the

semiclassical analysis of wigner 3j symbol we analyse the asymptotics of the wigner 3j symbol as a matrix element connecting eigenfunctions of a pair of integrable systems obtained by lifting the problem of the addition of angular momenta into the space of schwinger s oscillators a novel element is the appearance of compact lagrangian manifolds that are not tori due to the fact that the observables defining the quantum states are noncommuting these manifolds can be quantized by generalized bohr sommerfeld rules and yield all the correct quantum numbers the geometry of the classical angular momentum vectors emerges in a clear manner efficient methods for computing amplitude determinants in terms of poisson brackets are developed and illustrated

a combinatorial proof of the eisenbud goto conjecture for monomial curves and some simplicial semigroup rings abstract we will give a pure combinatorial proof of the eisenbud goto conjecture for arbitrary monomial curves moreover we will show that the conjecture holds for certain simplicial affine semigroup rings

conditional expectations on riesz spaces abstract conditional expectations operators acting on riesz spaces are shown to commute with a class of principal band projections using the above commutation property conditional expectation operators on riesz spaces are shown to be averaging operators here the theory of f algebras is used when defining multiplication on the riesz spaces this leads to the extension of these conditional expectation operators to their so called natural domains i e maximal domains for which the operators are both averaging operators and conditional expectations the natural domain is in many aspects analogous to l 1

generic projections the equations defining projective varieties and castelnuovo regularity for a reduced irreducible projective variety x of degree d and codimension e in mathbb p n the castelnuovo mumford regularity rm reg x is defined as the least k such that x is k regular i e h i mathbb p n mathcal i x k i 0 for i ge1 where mathcal i x subset cal o mathbb p n is the sheaf of ideals of x there is a long standing conjecture about k regularity see 5 rm reg x le d e 1 here we show that rm reg x le d e 1 10 for any smooth fivefold and rm reg x le d e 1 20 for any smooth sixfold by extending methods used in 10 furthermore we give a bound for the regularity of a reduced connected and equidimensional locally cohen macaulay curve or surface in terms of degree d codimension e and an arithmetic genus rho a see theorem 4 1

on the depth of the fiber cone of filtrations preprint enviat per a la seva publicacio en una revista cientifica journal of algebra 15 december 1997 volume 198 issue 2 pages 428 445 https doi org 10 1006 jabr 1997 7147

quantum symmetries and the weyl wigner product of group representations in the usual formulation of quantum mechanics groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex hilbert space in accordance with wigner s theorem in the phase space formulation they have real true unitary representations in the space of square integrable functions on phase space each such phase space representation is a weyl wigner product of the corresponding hilbert space representation with its contragredient and these can be recovered by factorizing the weyl wigner product however not every real unitary representation on phase space corresponds to a group of automorphisms so not every such representation is in the form of a weyl wigner product and can be factorized the conditions under which this is possible are examined examples are presented

minimal free resolutions of monomial curves in p3k abstract minimal free resolutions for prime ideals with generic zero t n 3 t n 3 n 1 0 t n 1 1 t n 3 n 2 0 t n 2 t n 3 1 n 1 n 2 n 3 positive integers n 1 n 2 n 3 1 are determined

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

initial ideals veronese subrings and rates of algebras abstract let s be a polynomial ring over an infinite field and let i be a homogeneous ideal of s let t d be a polynomial ring whose variables correspond to the monomials of degree d in s we study the initial ideals of the ideals v d i t d that define the veronese subrings of s i in suitable orders they are easily deduced from the initial ideal of i we show that in v d i is generated in degree max reg i d 2 where reg i is the regularity of the ideal i in other words the d th veronese subrings of any commutative graded ring s i has a grobner basis of degree max i d 2 we also give bounds on the regularity of i in terms of the degrees of the generators of in i and some combinatorial data this implies a version of backelin s theorem that high veronese subrings of any ring are homogeneous koszul algebras in the sense of priddy trans amer math soc 152 1970 39 60 we also give a general obstruction for a homogeneous ideal i s to have an initial ideal in i that is generated by quadrics beyond the obvious requirement that i itself should be generated by quadrics and the stronger statement that s i is koszul we use the obstruction to show that in certain dimensions a generic complete intersection of quadrics cannot have an initial ideal that is generated by quadrics for the application to backelin s theorem we require a result of backelin whose proof has never appeared we give a simple proof of a sharpened version bounding the rate of growth of the degrees of generators for syzygies of any multihomogenous module over a polynomial ring modulo an ideal generated by monomials following a method of bruns and herzog

lp spaces with respect to conditional expectation on riesz spaces recently labuschagne and watson introduced the space l2 t for a conditional expectation t with natural domain a riesz space l1 t the main purpose of this paper is to carry on with this process by introducing and investigate the spaces lp t with p 1

unbounded order convergence in dual spaces abstract a net x in a vector lattice x is said to be unbounded order convergent or uo convergent for short to x x if the net x x y converges to 0 in order for all y x in this paper we study unbounded order convergence in dual spaces of banach lattices let x be a banach lattice we prove that every norm bounded uo convergent net in x is w convergent iff x has order continuous norm and that every w convergent net in x is uo convergent iff x is atomic with order continuous norm we also characterize among order complete banach lattices the spaces in whose dual space every simultaneously uo and w convergent sequence converges weakly in norm

simplicial ideals 2 linear ideals and arithmetical rank abstract in the first part of this paper we study scrollers and linearly joined varieties scrollers were introduced in barile and morales 2004 bm4 linearly joined varieties are an extension of scrollers and were defined in eisenbud et al 2005 eghp there they proved that scrollers are defined by homogeneous ideals having a 2 linear resolution a particular class of varieties of important interest in classical geometry are cohen macaulay varieties of minimal degree they were classified geometrically by the successive contribution of del pezzo 1885 dp bertini 1907 b and xambo 1981 x and algebraically in barile and morales 2000 bm2 they appear naturally studying the fiber cone of a codimension two toric ideals morales 1995 m gimenez et al 1993 1999 gms1 gms2 barile and morales 1998 bm1 ha 2006 h ha and morales 2009 hm let s be a polynomial ring and i s a homogeneous ideal defining a sequence of linearly joined varieties we compute depth s i we prove that c v depth s i 1 where c v is the connectedness dimension of the algebraic set defined by i we characterize sets of generators of i and give an effective algorithm to find equations as an application we prove that ara i projdim s i in the case where v is a union of linear spaces in particular this applies to any square free monomial ideal having a 2 linear resolution in the case where v is a union of linear spaces the ideal i can be characterized by a tableau which is an extension of a ferrer or young tableau all these results are new and extend results in barile and morales 2004 bm4 eisenbud et al 2005 eghp

integral closures of ideals generated by regular sequences in particular our proposition contains s theorem 1 i as a special case in section 6 we shall make some remarks on theorem 2 in appendix 1 we shall give a proof of lemma 4 see section 1 for the sake of convenience this lemma is basic to our discussion of rees rings and the assertions in the lemma are all found in 9 if the ring a in the lemma is an integral domain in appendix 2 we shall make some remarks on the local cohomology modules of rees rings 390 0021 8693 88 83 00

the largest non vanishing degree of graded local cohomology modules abstract this paper gives characterizations for the largest non vanishing degree of the local cohomology modules of a graded ring s in terms of a reduction of s and of the associated graded ring of an ideal i in terms of any reduction of i as a consequence this invariant can be computed explicitly for the associated graded ring of any ideal generated by a d sequence and of ideals having small analytic deviation

powers of ideals generated by quadratic sequences huneke s conjecture that weak d sequences generate ideals of quadratic type is proved the proof suggests the definition of quadratic sequences which are more general than weak d sequences yet simpler to define and handle in addition to being just as useful we extend the theory of d sequences and weak d sequences to quadratic sequences results of costa on sequences of linear type are generalized an example of a two dimensional local domain in which every system of parameters is a d sequence in some order but which nevertheless fails to be buchsbaum is given a criterion is established for when equality holds in burch s inequality for an ideal generated by a quadratic sequence

asymptotic prime ideals of s2 filtrations abstract let a be a noetherian ring with total ring of fractions q a and s n z i n t n a noetherian graded ring such that a t 1 s q a t t 1 and s satisfies the s 2 property of serre under mild conditions on the ring a we study the behavior of the sets of associated prime ideals ass a i n a for n 1 in particular we consider the case when s is the s 2 ification of the extended rees algebra of an ideal i as applications we obtain several results regarding the asymptotic behavior of ass a i n for certain ideals of analytic deviation one we also prove several consequences about the symbolic powers of a prime ideal

on the structure of the fiber cone of ideals with analytic spread one for a given a local ring a m we study the fiber cone of ideals in a with analytic spread one in this case the fiber cone has a structure as a module over its noether normalization which is a polynomial ring in one variable over the residue field one may then apply the structure theorem for modules over a principal domain to get a complete description of the fiber cone as a module we analyze this structure in order to study and characterize in terms of the ideal itself the arithmetical properties and other numerical invariants of the fiber cone as multiplicity reduction number or castelnuovo mumford regularity

matrix cartan superdomains super toeplitz operators and quantization we present a general theory of non perturbative quantization of a class of hermitian symmetric supermanifolds the quantization scheme is based on the notion of a super toeplitz operator on a suitable z2 graded hilbert spaces of super holomorphic functions the quantized supermanifold arises as the c algebra generated by all such operators we prove that our quantization framework reproduces the invariant super poisson structure on the classical supermanifold as planck s constant tends to zero

on simplicial toric varieties which are set theoretic complete intersections abstract in this paper we prove in characteristic 0 every simplicial toric affine or projective variety with full parametrization is a set theoretic complete intersection this extends previous results by r hartshorne 1979 380 383 and t t moh 1985 217 220 in any characteristic every simplicial toric affine or projective variety with full parametrization is an almost set theoretic complete intersection this extends previous known results by m barile and m morales 1998 1907 1912 and a thoma to appear in any characteristic every simplicial toric affine or projective variety of codimension two is an almost set theoretic complete intersection moreover the proofs are constructive and the equations we find are binomial ones

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

binomial generation of the radical of a lattice ideal abstract let i l be a lattice ideal we provide a necessary and sufficient criterion under which a set of binomials in i l generates the radical of i l up to radical we apply our results to the problem of determining the minimal number of generators of i l or of the rad i l up to radical

integral degree of a ring reduction numbers and uniform artin rees numbers abstract the supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree a new invariant of the ring which is finite provided the ring has finite integral closure as a consequence one obtains bounds for the castelnuovo mumford regularity of the rees algebra and for the artin rees numbers

the wigner transformation is of finite order the wigner integral transformation which intertwines the twisted product and the composition of kernels is of order 24 indeed it commutes with and its sixth power equals the fourier cotransformation

on the depth of the associated graded ring of an ideal abstract let r be a local cohen macaulay ring let i be an r ideal and let g be the associated graded ring of i we give an estimate for the depth of g when g fails to be cohen macaulay we assume that i has a small reduction number and sufficiently good residual intersection properties and satisfies local conditions on the depth of some powers the main theorem unifies and generalizes several known results we also give conditions that imply the serre properties of the blow up rings

gorenstein graded rings associated to ideals let a be a noetherian local ring with the maximal ideal m and dim a d let i 6 a be an ideal in a and s hta i this article studies the question of when the associated graded ring g i i 0 i i is gorenstein to state our result we set up some notation let be an integer such that d and let j be a reduction of i generated by elements a1 a2 a we denote by rj i the reduction number of i with respect to j the analytic spread of i is i dim a m a g i then s i we always assume that the generating set a1 a2 a of j is a basic generating set for j in the sense of aberbach huneke and trung aht which means that jiaq is a reduction of iaq for all q v i with i hta q here let v i be a set of prime ideals in a containing i and ji a1 a2 ai for 0 i by aht 7 2 there always exists a basic generating set for j if the field a m is infinite let

quantum normal forms moyal star product and bohr sommerfeld approximation a normal form transformation is carried out on one dimensional quantum hamiltonians that transforms them into functions of the quantum harmonic oscillator the method works with the weyl transform or symbol of the hamiltonian the moyal star product is used to carry out the normal form transformation at the level of symbols diagrammatic techniques are developed for handling the expressions that result from higher order terms in the moyal series once the normal form is achieved the bohr sommerfeld formula for the eigenvalues including higher order corrections follows easily

toeplitz quantization of kahler manifolds ang gl n n limits for general compact kahler manifolds it is shown that both toeplitz quantization and geometric quantization lead to a well defined by operator norm estimates classical limit this generalizes earlier results of teh authors and klimek and lesniewski obtained for the tours and higher genus riemann surfaces respectively we thereby arrive at an approximation of the poisson algebra by a sequence of finitedimensional matrix algebrasgl n n

rees algebras of ideals having small analytic deviation in this article we identify two large families of ideals of a cohen macaulay sometimes gorenstein local ring whose rees algebras are cohen macaulay our main results imply for example that if r m is a regular local ring and p is a prime ideal of r such that p n is unmixed for all n 1 then the rees algebra r pt is cohen macaulay if either dim r p 2 o dim r p 3 r p is cohen macaulay and r p is integrally closed

cohen macaulay graded rings associated to ideals let g i be the associated graded ring of an ideal i in a cohen macaulay local ring a we give a sufficient condition for g i to be a cohen macaulay ring it is described in terms of the depths of a i n for finitely many n the reduction numbers of i q for certain prime ideals q and the artin nagata property of i in the sense of ulrich contemp math vol 159 pp 373 400 the main theorem unifies several results which are already known in this aspect of the theory although the statement of the main theorem is rather complicated we restate the conditions under special situations so that they are practical and simple

cohen macaulay rees algebras and their specialization the rees algebra of an ideal j in a commutative ring r is by definition the graded algebra where t is an indeterminate in this paper we are concerned with proving that certain rees algebras are cohen macaulay and with answering under strong hypotheses the question if r s n is a factor ring of s and i jr when is i r a specialization of j s that is when is the natural epimorphism r a j s r i r an isomorphism these questions have interest partly because if s and s j s are cohen macaulay then so is gr s s j j j 16 1 and under these hypotheses if n is perfect and r s j s i r then r and 7 1 r are cohen macaulay too thus gr r is cohen macaulay and its torsion freeness and normality for exmple can be characterized in terms of analytic spreads as in 161 see section 3 for details we deal with the specialization question in section 1 it is answered for the case where as above s and 2 j s are cohen macaulay and n is 202

ideals having the expected reduction number 1 introduction let r be a noetherian local ring with infinite residue field k and let be an r ideal when studying algebraic properties of the blow up of spec along v l it is often important to have good upper bounds for the reduction number of the ideal recall that an ideal c is a reduction of if the extension of rees algebras r jt c r it is module finite or equivalently if ir l j r for some r 0 32 the least such r is denoted by rj i a reduction is minimal if it is minimal with respect to inclusion and the reduction number r l of is defined as min o j a minimal reduction of finally the analytic spread i of is the krull dimension of the fiber ring r lt r k or equivalently the minimal number of generators jbi j of any minimal reduction j of 1 32 philosophically speaking j is a simplification of with the reduction number r l measuring how closely the two ideals are related of the numerous recent results about rees algebras and associated graded rings of ideals having small reduction number 18 19 38 35 12 13 14 4 3

syzygies of affine toric varieties we give a method for computing the syzygies of the coordinate ring r of an affine toric variety we show how the method works for dimension one and two cases cohen macaulay semigroups and for computing minimal generators of the defining ideal we show how to compute the depth of r and generalize a criterion for cohen macaulayness

on the uniqueness of the moyal structure of phase space functions uniqueness up to isomorphism of the moyal product and bracket of functions on as associative and lie deformations of the ordinary product and poisson bracket is known to follow under additional hypotheses using an integral formalism we show here that this result holds without these hypotheses

necessary and sufficient conditions for the cohen macaulayness of form rings abstract let a be a cohen macaulay local ring with an infinite residue field and let i a be an ideal of height h 0 supposing that depth a i n is high enough for certain values of n we give in this paper necessary and sufficient conditions for the form ring gr a i to be cohen macaulay with a invariant h or h 1

hilbert series of fiber cones of ideals with almost minimal mixed multiplicity abstract let r m be a cohen macaulay local ring and let i be an m primary ideal we introduce ideals of almost minimal mixed multiplicity which are analogues of ideals studied by j sally compositio math 40 1980 167 175 the main theorem describes the hilbert series of fiber cones of these ideals

an integral transform related to quantization ii some mathematical properties we study in more detail the mathematical properties of the integral transform relating the matrix elements between coherent states of a quantum operator to the corresponding classical function explicit families of hilbert spaces are constructed between which the integral transform is an isomorphism

artin nagata properties minimal multiplicities and depth of fiber cones abstract minimal values of multiplicities of ideals have a strong relation with the depth of blowup algebras in this paper we introduce the notion of goto minimal j multiplicity for ideals of maximal analytic spread in a cohen macaulay ring inspired by the work of s goto a jayanthan t puthenpurakal and j verma we study the interplay among this new notion the notion of minimal j multiplicity introduced by c polini and y xie and the cohen macaulayness of the fiber cone of ideals satisfying certain residual assumptions we are also able to provide a bound on the reduction number of ideals of goto minimal j multiplicity having either cohen macaulay associated graded algebra or linear decay in the depth of their powers

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

gorenstein associated graded rings of analytic deviation two ideals abstract this paper studies the question of when the associated graded ring g i n 0in in 1 of a certain ideal i in a local ring is gorenstein the main result implies for example that if a is a regular local ring 708 is a prime ideal in a with dim a p 2 and a p is a complete intersection in codimension one then the associated graded ring g p is gorenstein if and only if the reduction number of p is at most 1

normal cones of monomial primes we explicitly calculate the normal cones of all monomial primes which define the curves of the form tl tl 1 tl n where n 4 all of these normal cones are reduced and cohen macaulay and their reduction numbers are independent of the reduction these monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integrally closed substantial use was made of the computer algebra packages maple and macaulay2