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

• Record Type: Journal Article
• Authors: Pareschi, Giuseppe
• Is Part Of: International mathematics research notices. Volume 2021:Number 21(2021)
• Page Start: 16726
• Page End: 16735
• Publication Date: 2020-04-15
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa046
• Languages: English
• ISSNs: 1073-7928

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.