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arXiv · 2110.12419

Asymptotic vanishing of syzygies of algebraic varieties

Jinhyung Park
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Abstract

The purpose of this paper is to prove Ein--Lazarsfeld's conjecture on asymptotic vanishing of syzygies of algebraic varieties. This result, together with Ein--Lazarsfeld's asymptotic nonvanishing theorem, describes the overall picture of asymptotic behaviors of the minimal free resolutions of the graded section rings of line bundles on a projective variety as the positivity of the line bundles grows. Previously, Raicu reduced the problem to the case of products of three projective spaces, and we resolve this case here.

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Jinhyung Park. 2021-10-24. Asymptotic vanishing of syzygies of algebraic varieties. https://arxiv.org/abs/2110.12419

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