Effective Non-vanishing of Asymptotic Adjoint Syzygies

2012/03/31 by Xin Zhou, Zhou, Xin
Mathematics · #13D02 #14C99 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1204.0123

openalex publication_date 2012/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety, as the positivity of the embedding increases. Our purpose here is to show that for an adjoint type divisor B = K_X+ bA with b ≥ n+1, one can obtain an effective statement for arbitrary X which specializes to the statement for Veronese syzygies in the paper "Asymptotic Syzygies of Algebraic Varieties" by Ein and Lazarsfeld. We also give an answer to Problem 7.9 in that paper in this setting.

Citations

• Asymptotic syzygies of algebraic varieties

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