Singularities of Divisors of Low Degree on Simple Abelian Varieties

Abstract

Abstract It is known by the results of Kollár, Ein, Lazarsfeld, Hacon, and Debarre that effective divisors representing principal and other low-degree polarizations on complex abelian varieties have mild singularities. In this note, we extend these results to all polarizations of degree $<g$ on simple $g$-dimensional abelian varieties, settling a conjecture of Debarre and Hacon.