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.
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