The Albanese morphism for hyperelliptic varieties

Pieter Belmans; Andreas Demleitner; Pedro Núñez

doi:10.1016/j.indag.2025.10.004

The Albanese morphism for hyperelliptic varieties

Pieter Belmans^*
, Andreas Demleitner
, Pedro Núñez

^*Corresponding author for this work

Sub Fundamental Mathematics

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Journal	Indagationes Mathematicae
DOIs	https://doi.org/10.1016/j.indag.2025.10.004
Publication status	E-pub ahead of print - 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s).

Keywords

Albanese morphism
Derived categories
Hyperelliptic varieties

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10.1016/j.indag.2025.10.004Licence: CC BY

Cite this

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title = "The Albanese morphism for hyperelliptic varieties",

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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AU - Demleitner, Andreas

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AB - 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.

KW - Albanese morphism

KW - Derived categories

KW - Hyperelliptic varieties

UR - https://www.scopus.com/pages/publications/105025052732

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DO - 10.1016/j.indag.2025.10.004

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JO - Indagationes Mathematicae

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ER -

The Albanese morphism for hyperelliptic varieties

Abstract

Bibliographical note

Keywords

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