Asymptotic syzygies of algebraic varieties

Lawrence Ein; Robert Lazarsfeld

doi:10.1007/s00222-012-0384-5

Asymptotic syzygies of algebraic varieties

Lawrence Ein
, Robert Lazarsfeld

Mathematics

University of Illinois at Chicago

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	603-646
Number of pages	44
Journal	Inventiones Mathematicae
Volume	190
Issue number	3
DOIs	https://doi.org/10.1007/s00222-012-0384-5
State	Published - Dec 2012

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AB - 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.

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Asymptotic syzygies of algebraic varieties

Abstract

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