Singularities of Divisors of Low Degree on Simple Abelian Varieties. (15th April 2020) - Pareschi, Giuseppe
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.