A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture

探索Buchsbaum–Eisenbud–Horrocks猜想的局部变体

Exploring a local variant of the Buchsbaum--Eisenbud--Horrocks conjecture

本文针对完全交奇点研究中提出的Buchsbaum–Eisenbud–Horrocks猜想的变体，证明其部分成立、一般情形不成立，并提出该猜想的局部变体。

Buchsbaum-Eisenbud complexes of OI-modules

We extend the theory of Koszul and Buchsbaum-Eisenbud complexes to modules over commutative OI-algebras and show that they still have the familiar properties of the classical complexes. In particular, the OI-complexes are generically acyclic and often provide width-wise minimal free resolutions.

A structure result for Gorenstein algebras of odd codimension

The famous structure theorem of Buchsbaum and Eisenbud gives a complete characterization of Gorenstein ideals of codimension 3 and their minimal free resolutions. We generalize the ideas of Buchsbaum and Eisenbud from Gorenstein ideals to Gorenstein algebras and present a description of Gorenstein algebras of any odd codimension. As an application we study the canonical ring of a numerical Godeaux surface.

The Horrocks correspondence for coherent sheaves on projective spaces

We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra Koszul dual to the homogeneous coordinate algebra of the projective space. We also relate these complexes to the Tate resolutions of the respective sheaves. In this way, we extend from vector bundles to coherent sheaves the results of Coandă and Trautmann [Trans. AMS 385 (2005)], which interpret in terms of the BGG correspondence the results of Trautmann [Math…

del Pezzo簇合子的一个结构定理

A structure theorem for syzygies of del Pezzo varieties

本文利用Buchsbaum-Eisenbud结构定理，证明了定义del Pezzo簇的二次型间最高线性合子可表示为元素为线性形式楔积的斜对称矩阵的列。

Total Betti numbers of modules of finite projective dimension

The Buchsbaum-Eisenbud-Horrocks Conjecture predicts that if M is a non-zero module of finite length and finite projective dimension over a local ring R of dimension d, then the i-th Betti number of M is at least d choose i. This conjecture implies that the sum of all the Betti numbers of such a module must be at least 2^d. We prove the latter holds in a large number of cases.