---
_id: '66336'
abstract:
- lang: eng
  text: We contribute to the foundations of tropical geometry with a view towards
    formulating tropical moduli problems, and with the moduli space of curves as our
    main example. We propose a moduli functor for the moduli space of curves and show
    that it is representable by a geometric stack over the category of rational polyhedral
    cones. In this framework the natural forgetful morphisms between moduli spaces
    of curves with marked points function as universal curves. Our approach to tropical
    geometry permits tropical moduli problems---moduli of curves or otherwise---to
    be extended to logarithmic schemes. We use this to construct a smooth tropicalization
    morphism from the moduli space of algebraic curves to the moduli space of tropical
    curves, and we show that this morphism commutes with all of the tautological morphisms.
author:
- first_name: Renzo
  full_name: Cavalieri, Renzo
  last_name: Cavalieri
- first_name: Melody
  full_name: Chan, Melody
  last_name: Chan
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Jonathan
  full_name: Wise, Jonathan
  last_name: Wise
citation:
  ama: Cavalieri R, Chan M, Ulirsch M, Wise J. A moduli stack of tropical curves.
    <i>arXiv:170403806</i>. Published online 2017. doi:<a href="https://doi.org/10.1017/fms.2020.16">10.1017/fms.2020.16</a>
  apa: Cavalieri, R., Chan, M., Ulirsch, M., &#38; Wise, J. (2017). A moduli stack
    of tropical curves. <i>ArXiv:1704.03806</i>. <a href="https://doi.org/10.1017/fms.2020.16">https://doi.org/10.1017/fms.2020.16</a>
  bibtex: '@article{Cavalieri_Chan_Ulirsch_Wise_2017, title={A moduli stack of tropical
    curves}, DOI={<a href="https://doi.org/10.1017/fms.2020.16">10.1017/fms.2020.16</a>},
    journal={arXiv:1704.03806}, author={Cavalieri, Renzo and Chan, Melody and Ulirsch,
    Martin and Wise, Jonathan}, year={2017} }'
  chicago: Cavalieri, Renzo, Melody Chan, Martin Ulirsch, and Jonathan Wise. “A Moduli
    Stack of Tropical Curves.” <i>ArXiv:1704.03806</i>, 2017. <a href="https://doi.org/10.1017/fms.2020.16">https://doi.org/10.1017/fms.2020.16</a>.
  ieee: 'R. Cavalieri, M. Chan, M. Ulirsch, and J. Wise, “A moduli stack of tropical
    curves,” <i>arXiv:1704.03806</i>, 2017, doi: <a href="https://doi.org/10.1017/fms.2020.16">10.1017/fms.2020.16</a>.'
  mla: Cavalieri, Renzo, et al. “A Moduli Stack of Tropical Curves.” <i>ArXiv:1704.03806</i>,
    2017, doi:<a href="https://doi.org/10.1017/fms.2020.16">10.1017/fms.2020.16</a>.
  short: R. Cavalieri, M. Chan, M. Ulirsch, J. Wise, ArXiv:1704.03806 (2017).
date_created: 2026-07-08T07:07:13Z
date_updated: 2026-07-08T08:26:17Z
doi: 10.1017/fms.2020.16
external_id:
  arxiv:
  - '1704.03806'
language:
- iso: eng
publication: arXiv:1704.03806
status: public
title: A moduli stack of tropical curves
type: journal_article
user_id: '82981'
year: '2017'
...