Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909036593545216 |
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| author | Gross, Andreas Kaur, Inder Ulirsch, Martin Werner, Annette |
| author_facet | Gross, Andreas Kaur, Inder Ulirsch, Martin Werner, Annette |
| contents | Let $A$ be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semihomogeneous vector bundles on $A$ from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For $H=0$ our moduli space may be identified with the moduli space $M_{0,r}(A)$ of semistable vector bundles with vanishing Chern classes on $A$. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of $A$ onto $M_{0,r}(A)$, which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of $M_{0,r}(A)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12980 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization Gross, Andreas Kaur, Inder Ulirsch, Martin Werner, Annette Algebraic Geometry Let $A$ be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semihomogeneous vector bundles on $A$ from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For $H=0$ our moduli space may be identified with the moduli space $M_{0,r}(A)$ of semistable vector bundles with vanishing Chern classes on $A$. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of $A$ onto $M_{0,r}(A)$, which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of $M_{0,r}(A)$. |
| title | Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.12980 |