---
_id: '66317'
abstract:
- lang: eng
  text: In this article we provide a stack-theoretic framework to study the universal
    tropical Jacobian over the moduli space of tropical curves. We develop two approaches
    to the process of tropicalization of the universal compactified Jacobian over
    the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean
    analytic point of view. The central result from both points of view is that the
    tropicalization of the universal compactified Jacobian is the universal tropical
    Jacobian and that the tropicalization maps in each of the two contexts are compatible
    with the tautological morphisms. In a sequel we will use the techniques developed
    here to provide explicit polyhedral models for the logarithmic Picard variety.
author:
- first_name: Margarida
  full_name: Melo, Margarida
  last_name: Melo
- first_name: Samouil
  full_name: Molcho, Samouil
  last_name: Molcho
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Filippo
  full_name: Viviani, Filippo
  last_name: Viviani
citation:
  ama: Melo M, Molcho S, Ulirsch M, Viviani F. Tropicalization of the universal Jacobian.
    <i>arXiv:210804711</i>. Published online 2021. doi:<a href="https://doi.org/doi.org/10.46298/epiga.2022.8352">doi.org/10.46298/epiga.2022.8352</a>
  apa: Melo, M., Molcho, S., Ulirsch, M., &#38; Viviani, F. (2021). Tropicalization
    of the universal Jacobian. <i>ArXiv:2108.04711</i>. <a href="https://doi.org/doi.org/10.46298/epiga.2022.8352">https://doi.org/doi.org/10.46298/epiga.2022.8352</a>
  bibtex: '@article{Melo_Molcho_Ulirsch_Viviani_2021, title={Tropicalization of the
    universal Jacobian}, DOI={<a href="https://doi.org/doi.org/10.46298/epiga.2022.8352">doi.org/10.46298/epiga.2022.8352</a>},
    journal={arXiv:2108.04711}, author={Melo, Margarida and Molcho, Samouil and Ulirsch,
    Martin and Viviani, Filippo}, year={2021} }'
  chicago: Melo, Margarida, Samouil Molcho, Martin Ulirsch, and Filippo Viviani. “Tropicalization
    of the Universal Jacobian.” <i>ArXiv:2108.04711</i>, 2021. <a href="https://doi.org/doi.org/10.46298/epiga.2022.8352">https://doi.org/doi.org/10.46298/epiga.2022.8352</a>.
  ieee: 'M. Melo, S. Molcho, M. Ulirsch, and F. Viviani, “Tropicalization of the universal
    Jacobian,” <i>arXiv:2108.04711</i>, 2021, doi: <a href="https://doi.org/doi.org/10.46298/epiga.2022.8352">doi.org/10.46298/epiga.2022.8352</a>.'
  mla: Melo, Margarida, et al. “Tropicalization of the Universal Jacobian.” <i>ArXiv:2108.04711</i>,
    2021, doi:<a href="https://doi.org/doi.org/10.46298/epiga.2022.8352">doi.org/10.46298/epiga.2022.8352</a>.
  short: M. Melo, S. Molcho, M. Ulirsch, F. Viviani, ArXiv:2108.04711 (2021).
date_created: 2026-07-08T06:44:47Z
date_updated: 2026-07-08T08:24:37Z
doi: doi.org/10.46298/epiga.2022.8352
external_id:
  arxiv:
  - '2108.04711'
language:
- iso: eng
publication: arXiv:2108.04711
status: public
title: Tropicalization of the universal Jacobian
type: journal_article
user_id: '82981'
year: '2021'
...