The Albanese morphism for hyperelliptic varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929600572948480 |
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| author | Belmans, Pieter Demleitner, Andreas Núñez, Pedro |
| author_facet | Belmans, Pieter Demleitner, Andreas Núñez, Pedro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14814 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Albanese morphism for hyperelliptic varieties Belmans, Pieter Demleitner, Andreas Núñez, Pedro Algebraic Geometry 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. |
| title | The Albanese morphism for hyperelliptic varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2411.14814 |