The equations of singular loci of ample divisors on (subvarieties of) abelian varieties

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.

Keywords

• Singular loci
• Continuously global generation
• Bundle of differential operators