Asymptotic nonvanishing of syzygies of algebraic varieties

2023/05/25 by Jinhyung Park, Park, Jinhyung · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.15802

openalex publication_date 2023/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish precise nonvanishing results for asymptotic syzygies of smooth projective varieties. This refines Ein-Lazarsfeld's asymptotic nonvanishing theorem. Combining with the author's previous asymptotic vanishing result, we completely determine the asymptotic shapes of the minimal free resolutions of the graded section modules of a line bundle on a smooth projective variety as the positivity of the embedding line bundle grows.

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