Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese Dimension

Abstract

Let $X$ be a smooth projective complex variety of maximal Albanese dimension, and let $L\to X$ be a big line bundle. We prove that the moving Seshadri constants of the pull-backs of $L$ to suitable finite abelian étale covers of $X$ are arbitrarily large. As an application, given any integer $k\ge 1$, there exists an abelian étale cover $p:X^{\prime }\to X$ such that the adjoint system $|K_{X^{\prime }}+p^{\ast }L|$ separates $k$-jets away from the augmented base locus of $p^{\ast }L$, and the exceptional locus of the pull-back of the Albanese map of $X$ under $p$.

Some changes and typos corrected following referee's report. To appear in Asian J. Math., 19 pages