Asymptotic syzygies of algebraic varieties

• 成果类型: Article
• 署名作者: Ein, Lawrence; Lazarsfeld, Robert
• 署名单位: University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0384-5
• 发表日期: 2012
• 页码: 603-646
• 关键词: koszul cohomology; multigraded regularity; conjecture; geometry; CURVES

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.