---
_id: '66309'
abstract:
- lang: eng
  text: 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 $M_{0,r}(A)$.
author:
- first_name: Andreas
  full_name: Gross, Andreas
  last_name: Gross
- first_name: Inder
  full_name: Kaur, Inder
  last_name: Kaur
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Annette
  full_name: Werner, Annette
  last_name: Werner
citation:
  ama: 'Gross A, Kaur I, Ulirsch M, Werner A. Semi-homogeneous vector bundles on abelian
    varieties: moduli spaces and their tropicalization. <i>arXiv:231212980</i>. Published
    online 2023. doi:<a href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>'
  apa: 'Gross, A., Kaur, I., Ulirsch, M., &#38; Werner, A. (2023). Semi-homogeneous
    vector bundles on abelian varieties: moduli spaces and their tropicalization.
    <i>ArXiv:2312.12980</i>. <a href="https://doi.org/10.1017/S2949764726100228">https://doi.org/10.1017/S2949764726100228</a>'
  bibtex: '@article{Gross_Kaur_Ulirsch_Werner_2023, title={Semi-homogeneous vector
    bundles on abelian varieties: moduli spaces and their tropicalization}, DOI={<a
    href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>},
    journal={arXiv:2312.12980}, author={Gross, Andreas and Kaur, Inder and Ulirsch,
    Martin and Werner, Annette}, year={2023} }'
  chicago: 'Gross, Andreas, Inder Kaur, Martin Ulirsch, and Annette Werner. “Semi-Homogeneous
    Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.”
    <i>ArXiv:2312.12980</i>, 2023. <a href="https://doi.org/10.1017/S2949764726100228">https://doi.org/10.1017/S2949764726100228</a>.'
  ieee: 'A. Gross, I. Kaur, M. Ulirsch, and A. Werner, “Semi-homogeneous vector bundles
    on abelian varieties: moduli spaces and their tropicalization,” <i>arXiv:2312.12980</i>,
    2023, doi: <a href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>.'
  mla: 'Gross, Andreas, et al. “Semi-Homogeneous Vector Bundles on Abelian Varieties:
    Moduli Spaces and Their Tropicalization.” <i>ArXiv:2312.12980</i>, 2023, doi:<a
    href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>.'
  short: A. Gross, I. Kaur, M. Ulirsch, A. Werner, ArXiv:2312.12980 (2023).
date_created: 2026-07-08T06:24:15Z
date_updated: 2026-07-08T08:29:27Z
doi: 10.1017/S2949764726100228
external_id:
  arxiv:
  - '2312.12980'
language:
- iso: eng
publication: arXiv:2312.12980
status: public
title: 'Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their
  tropicalization'
type: journal_article
user_id: '82981'
year: '2023'
...