Filip Chindea: ACM bundles on abelian surfaces of Picard rank 4, 445-448

Abstract:

Let $X$ be an abelian surface. It is a recent result due to Beauville that all polarized abelian surfaces possess an Ulrich (hence ACM) bundle of rank $2$. However, the case of ACM line bundles was left open. In this note we solve the problem in the affirmative by discussing their existence on a member of the isogeny class of any $X$ in the case of Picard number $4$, and finally extend to any such $X$.

Key Words: ACM, vector bundle, abelian surface, ampleness, isogeny.

2020 Mathematics Subject Classification: Primary 14J60; Secondary 14K22.

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