A quick proof of nonvanishing for asymptotic syzygies

Lawrence Ein; Daniel Erman; Robert Lazarsfeld

doi:10.14231/AG-2016-010

A quick proof of nonvanishing for asymptotic syzygies

Lawrence Ein
, Daniel Erman
, Robert Lazarsfeld

Mathematics

University of Illinois at Chicago
University of Wisconsin-Madison

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

13 Scopus citations

Abstract

We give a quick new approach to proving the main cases of the nonvanishing theorems of the first and third authors concerning the asymptotic behavior of the syzygies of a projective variety as the positivity of the embedding line bundle grows. In particular, we recover and extend the statements for Veronese syzygies, and we establish an effective result for projectively Cohen{Macaulay varieties.

Original language	English
Pages (from-to)	211-222
Number of pages	12
Journal	Algebraic Geometry
Volume	3
Issue number	2
DOIs	https://doi.org/10.14231/AG-2016-010
State	Published - Mar 1 2016

Keywords

Free resolutions
Syzygies
Very positive embeddings

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10.14231/AG-2016-010

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AU - Lazarsfeld, Robert

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N2 - We give a quick new approach to proving the main cases of the nonvanishing theorems of the first and third authors concerning the asymptotic behavior of the syzygies of a projective variety as the positivity of the embedding line bundle grows. In particular, we recover and extend the statements for Veronese syzygies, and we establish an effective result for projectively Cohen{Macaulay varieties.

AB - We give a quick new approach to proving the main cases of the nonvanishing theorems of the first and third authors concerning the asymptotic behavior of the syzygies of a projective variety as the positivity of the embedding line bundle grows. In particular, we recover and extend the statements for Veronese syzygies, and we establish an effective result for projectively Cohen{Macaulay varieties.

KW - Free resolutions

KW - Syzygies

KW - Very positive embeddings

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JO - Algebraic Geometry

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ER -

A quick proof of nonvanishing for asymptotic syzygies

Abstract

Keywords

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