SHORT KOSZUL MODULES

被引：3

作者：

Avramov, Luchezar L. ^{[1
]}

Iyengar, Srikanth B. ^{[1
]}

Sega, Liana M. ^{[2
]}

机构：

[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[2] Univ Missouri, Dept Math & Stat, Kansas City, MO 64110 USA

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2010年 / 2卷 / 03期

基金：

美国国家科学基金会;

关键词：

Koszul algebras; Koszul module;

D O I：

10.1216/JCA-2010-2-3-249

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This article is concerned with graded modules M with linear resolutions over a standard graded algebra R. It is proved that if such an M has Hilbert series H-M (s) of the form ps(d) + qs(d+1), then the algebra R is Koszul; if, in addition, M has constant Betti numbers, then H-R(s) = 1+es+(e - 1)s(2) When H-R(s) = 1 + es + rs(2) with r <= e - 1, and R is Gorenstein or e = r + 1 <= 3, it is proved that generic R-modules with q <= (e - 1)p are linear.

引用

页码：249 / 279

页数：31

共 20 条

[1]

[Anonymous], 1965, PUBL MATH-PARIS

[2]

[Anonymous], 2005, Univ. Lecture Ser.

[3] Free resolutions over short local rings [J].