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# Asian Journal of Mathematics

## Volume 25 (2021)

### Number 2

### Moving Seshadri constants, and coverings of varieties of maximal Albanese dimension

Pages: 305 – 320

DOI: https://dx.doi.org/10.4310/AJM.2021.v25.n2.a8

#### Authors

#### 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 $k \geq 1$, there exists an abelian étale cover $p : X^\prime \to X$ such that the adjoint system $\lvert K_{X^\prime} + p^\ast L \rvert$ separates $k$‑jets away from the augmented base locus of $p^\ast L$, and the exceptional locus of the pullback of the Albanese map of $X$ under $p$.

#### Keywords

moving Seshadri constants, varieties of maximal Albanese dimension, separation of $k$-jets

#### 2010 Mathematics Subject Classification

14C25, 32J25

The second-named author was partially supported by SIR 2014 AnHyC: “Analytic aspects in complex and hypercomplex geometry” (code RBSI14DYEB), Grant 261756 of the Research Council of Norway, and the Simons Foundation.

Received 17 July 2019

Accepted 27 August 2020

Published 15 October 2021