相关论文: A genus explanation of the Buchsbaum-Rim multiplic…

We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero…

Over a regular local ring of dimension two with maximal ideal m, we study the Buchsbaum-Rim multiplicity of a finitely generated module M of finite colength in a free module F. First, we investigate the colength of an m-primary ideal and…

This paper begins by introducing and characterizing Buchsbaum-Rim sheaves on $Z = \Proj R$ where $R$ is a graded Gorenstein K-algebra. They are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between…

We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential $p$-forms of a…

The associated Buchsbaum-Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization of the classical Hilbert-Samuel multiplicity of an ideal. In this article, we…

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous $k$-algebras $A$ in terms of the dimension $d$, the codimension $c$, the initial degree $q$, and the length of the local cohomology modules of $A$. Next,…

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…

In the appendix of the famous book "Commutative Algebra with a View Towards Algebraic Geometry" one can find an infinite family of complexes indexed by integers. This family includes Eagon-Northcott and Buschsbaum-Rim complexes. The…

A three-term complex of free modules over a local ring determines a mixed Koszul complex, whose Euler characteristic can be expressed by mixed multiplicities. As an application, we offer a simple formula for the index of a holomorphic…

We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology…

A class of simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum*…

We identify a close relationship between stable sheaf cohomology for polynomial functors applied to the cotangent bundle on projective space, and Koszul--Ringel duality on the category of strict polynomial functors as described in the work…

We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a two-dimensional manifold M the algebra is Koszul if and…

In this survey paper, we present \v{C}ech and sheaf cohomologies -- themes that were presented by Koszul in University of S\~ao Paulo during his visit in the late 1950s -- we present expansions for categories of generalized sheaves (i.e,…

In this article we prove that the Buchsbaum-Rim multiplicity $e(F/N)$ of a parameter module $N$ in a free module $F=A^r$ is bounded above by the colength $\ell_A(F/N)$. Moreover, we prove that once the equality $\ell_A(F/N)=e(F/N)$ holds…

Let $K$ be a field of characteristic zero. Let $R = K[X_0, X_1,\ldots,X_n]$ be standard graded. Let $A_{n+1}(K)$ be the $(n + 1)^{th}$ Weyl algebra over $K$. Let $I$ be a homogeneous ideal of $R$ and let $M = H^i_I(R)$ for some $i \geq 0$.…

We construct a canonical isomorphism between the Bethe algebra acting on a multiplicity space of a tensor product of evaluation gl_N[t]-modules and the scheme-theoretic intersection of suitable Schubert varieties. Moreover, we prove that…

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a…

We prove the results about mixed Buchsbaum--Rim multiplicities announced in (9.10)(ii) on p.224 of our recent paper [J.Alg.(1994)], including a general mixed-multiplicity formula. In addition, we identify these multiplicities as the…

Let $(R, \mathfrak m)$ be a $d$-dimensional Noetherian local ring and $E$ a finitely generated $R$-submodule of a free module $R^p.$ In this work we introduce a multiplicity sequence $c_k(E), k=0,..., d+p-1$ for $E$ that generalize the…