Asymptotic syzygies of algebraic varieties

被引：46
作者：
Ein, Lawrence [2 ]
Lazarsfeld, Robert [1 ]
机构：
[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
[2] Univ Illinois, Dept Math, Chicago, IL 60607 USA
来源：
INVENTIONES MATHEMATICAE | 2012年 / 190卷 / 03期
基金：
美国国家科学基金会;
关键词：
KOSZUL COHOMOLOGY; MULTIGRADED REGULARITY; CONJECTURE; GEOMETRY; CURVES;
D O I：
10.1007/s00222-012-0384-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero in almost all degrees allowed by Castelnuovo-Mumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal.
引用
收藏
页码：603 / 646
页数：44
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