---
_id: '66352'
abstract:
- lang: eng
  text: Hassett's moduli spaces of weighted stable curves form an important class
    of alternate modular compactifications of the moduli space of smooth curves with
    marked points. In this article we define a tropical analogue of these moduli spaces
    and show that the naive set-theoretic tropicalization map can be identified with
    a natural deformation retraction onto the non-Archimedean skeleton. This result
    generalizes work of Abramovich, Caporaso, and Payne treating the Deligne-Knudsen-Mumford
    compactification of the moduli space of smooth curves with marked points. We also
    study tropical analogues of the tautological maps, investigate the dependence
    of the tropical moduli spaces on the weight data, and consider the example of
    Losev-Manin spaces.
author:
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
citation:
  ama: Ulirsch M. Tropical geometry of moduli spaces of weighted stable curves. <i>arXiv:14056940</i>.
    Published online 2014. doi:<a href="https://doi.org/10.1112/jlms/jdv032">10.1112/jlms/jdv032</a>
  apa: Ulirsch, M. (2014). Tropical geometry of moduli spaces of weighted stable curves.
    <i>ArXiv:1405.6940</i>. <a href="https://doi.org/10.1112/jlms/jdv032">https://doi.org/10.1112/jlms/jdv032</a>
  bibtex: '@article{Ulirsch_2014, title={Tropical geometry of moduli spaces of weighted
    stable curves}, DOI={<a href="https://doi.org/10.1112/jlms/jdv032">10.1112/jlms/jdv032</a>},
    journal={arXiv:1405.6940}, author={Ulirsch, Martin}, year={2014} }'
  chicago: Ulirsch, Martin. “Tropical Geometry of Moduli Spaces of Weighted Stable
    Curves.” <i>ArXiv:1405.6940</i>, 2014. <a href="https://doi.org/10.1112/jlms/jdv032">https://doi.org/10.1112/jlms/jdv032</a>.
  ieee: 'M. Ulirsch, “Tropical geometry of moduli spaces of weighted stable curves,”
    <i>arXiv:1405.6940</i>, 2014, doi: <a href="https://doi.org/10.1112/jlms/jdv032">10.1112/jlms/jdv032</a>.'
  mla: Ulirsch, Martin. “Tropical Geometry of Moduli Spaces of Weighted Stable Curves.”
    <i>ArXiv:1405.6940</i>, 2014, doi:<a href="https://doi.org/10.1112/jlms/jdv032">10.1112/jlms/jdv032</a>.
  short: M. Ulirsch, ArXiv:1405.6940 (2014).
date_created: 2026-07-08T07:24:26Z
date_updated: 2026-07-08T08:42:44Z
doi: 10.1112/jlms/jdv032
external_id:
  arxiv:
  - '1405.6940'
language:
- iso: eng
publication: arXiv:1405.6940
status: public
title: Tropical geometry of moduli spaces of weighted stable curves
type: journal_article
user_id: '82981'
year: '2014'
...