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arXiv · 1501.01612

A quick proof of nonvanishing for asymptotic syzygies

Lawrence Ein·Daniel Erman·Robert Lazarsfeld
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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.

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Lawrence Ein, Daniel Erman, Robert Lazarsfeld. 2016-09-11. A quick proof of nonvanishing for asymptotic syzygies. https://doi.org/10.14231/ag-2016-010

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