---
_id: '66336'
abstract:
- lang: eng
  text: "<jats:p>We contribute to the foundations of tropical geometry with a view
    toward 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.</jats:p>\r\n\t
    \ <jats:p>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.</jats:p>"
article_number: e23
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>Forum of Mathematics, Sigma</i>. 2020;8. 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. (2020). A MODULI STACK
    OF TROPICAL CURVES. <i>Forum of Mathematics, Sigma</i>, <i>8</i>, Article e23.
    <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_2020, title={A MODULI STACK OF TROPICAL
    CURVES}, volume={8}, DOI={<a href="https://doi.org/10.1017/fms.2020.16">10.1017/fms.2020.16</a>},
    number={e23}, journal={Forum of Mathematics, Sigma}, publisher={Cambridge University
    Press (CUP)}, author={Cavalieri, Renzo and Chan, Melody and Ulirsch, Martin and
    Wise, Jonathan}, year={2020} }'
  chicago: Cavalieri, Renzo, Melody Chan, Martin Ulirsch, and Jonathan Wise. “A MODULI
    STACK OF TROPICAL CURVES.” <i>Forum of Mathematics, Sigma</i> 8 (2020). <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>Forum of Mathematics, Sigma</i>, vol. 8, Art. no. e23, 2020, 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>Forum of Mathematics,
    Sigma</i>, vol. 8, e23, Cambridge University Press (CUP), 2020, 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, Forum of Mathematics, Sigma 8
    (2020).
date_created: 2026-07-08T07:07:13Z
date_updated: 2026-07-09T07:06:55Z
doi: 10.1017/fms.2020.16
intvolume: '         8'
language:
- iso: eng
publication: Forum of Mathematics, Sigma
publication_identifier:
  issn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press (CUP)
status: public
title: A MODULI STACK OF TROPICAL CURVES
type: journal_article
user_id: '82981'
volume: 8
year: '2020'
...