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

Luca F. Di Cerbo; Luigi Lombardi

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arXiv · 1902.04098

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

Luca F. Di Cerbo·Luigi Lombardi

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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 \'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 $p$.

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BibTeX RIS

Luca F. Di Cerbo, Luigi Lombardi. 2019-02-11. Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese Dimension. https://arxiv.org/abs/1902.04098

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