The Equations of Singular Loci of Ample Divisors on (Subvarieties of) Abelian Varieties

2008/03/24 by Luigi Lombardi, Lombardi, Luigi, Francesco Malaspina +1
Computer Science · Mathematics · Physics and Astronomy · #14F05 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0803.3444

openalex publication_date 2008/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system |L| of an ample line bundle on a complex abelian variety. We prove an effective result on their (continuous) global generation, after suitable twists by powers of L. Moreover we show that similar results hold for subvarieties of a complex abelian variety.

Citations

• Regularity on abelian varieties III: relationship with Generic Vanishing and applications

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