Line-filtered rank-two ACM bundles on abelian varieties of Picard rank one

Abstract

Let $A$ be a complex abelian variety of dimension $g\ge 2$ with $\NS(A)\cong\ZZ$ generated by an ample class $L$. We classify, up to twist by powers of $L$, the rank-two arithmetically Cohen--Macaulay bundles on $A$ with empty defect: they are sums of two ACM line bundles or nonsplit self-extensions of a nontrivial degree-zero line bundle. We also show none is Ulrich.