A quick proof of nonvanishing for asymptotic syzygies
Algebraic Geometry
2018-04-30 v2 Commutative Algebra
Abstract
We give a quick new approach to the main cases of the nonvanishing theorems of first and third authors concerning the asymptotic behavior of the syzygies of a projective variety as the positivity of the embedding line bundle grows. Specifically, we present a surprisingly elementary and concrete proof of the asymptotic nonvanishing of Veronese syzygies, and we obtain effective results for arithmetically Cohen-Macaulay varieties. The idea is that one can reduce the statements to some simple computations with monomials.
Keywords
Cite
@article{arxiv.1501.01612,
title = {A quick proof of nonvanishing for asymptotic syzygies},
author = {Lawrence Ein and Daniel Erman and Robert Lazarsfeld},
journal= {arXiv preprint arXiv:1501.01612},
year = {2018}
}
Comments
Typos corrected. Section numbering changed to conform to published version