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

TL;DR

This paper investigates the equations defining the singular loci of ample divisors on complex abelian varieties and their subvarieties, providing effective results on their global generation after certain twists.

Contribution

It introduces new effective criteria for the global generation of ideal sheaves associated to singular loci on abelian varieties and subvarieties, extending previous understanding.

Findings

Effective global generation results for ideal sheaves of singular loci

Extension of results to subvarieties of abelian varieties

Conditions under which twists by powers of L ensure generation

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.