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arXiv · 2411.14814

The Albanese morphism for hyperelliptic varieties

Pieter Belmans·Andreas Demleitner·Pedro Núñez
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Abstract

We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient $X$ of an abelian variety $A$ by a finite group $G$ acting freely and not only by translations, by giving a description of the Albanese variety and the Albanese fibers in terms of $A$ and $G$. In particular, the fibers are themselves abelian or hyperelliptic varieties, and we investigate which can occur in explicit examples. As an application we show that the derived category of $X$ is indecomposable in certain cases.

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Pieter Belmans, Andreas Demleitner, Pedro Núñez. 2024-11-22. The Albanese morphism for hyperelliptic varieties. https://arxiv.org/abs/2411.14814

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