Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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L. Di Cerbo - L. Lombardi

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

created by daniele on 26 Feb 2020



Inserted: 26 feb 2020
Last Updated: 26 feb 2020

Year: 2019

ArXiv: 1902.04098 PDF


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 \'etale covers of $X$ are arbitrarily large. As an application, given any integer $k\geq 1$, there exists an abelian \'etale cover $p\colon X' \to X$ such that the adjoint system $\big
K_{X'} + p^*L \big
$ separates $k$-jets away from the augmented base locus of $p^*L$, and the exceptional locus of the pull-back of the Albanese map of $X$ under $p$.

Tags: SIR2014-AnHyC

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