The basepoint-freeness threshold of a very general abelian surface

2021/07/05 by Andrés Rojas, Rojas, Andrés
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2107.01896

openalex publication_date 2021/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For abelian surfaces of Picard rank 1, we perform explicit computations of the cohomological rank functions of the ideal sheaf of one point, and in particular of the basepoint-freeness threshold. Our main tool is the relation between cohomological rank functions and Bridgeland stability. In virtue of recent results of Caucci and Ito, these computations provide new information on the syzygies of polarized abelian surfaces.

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