---
_id: '66350'
abstract:
- lang: eng
  text: We study whether a given tropical curve $Γ$ in $\mathbb{R}^n$ can be realized
    as the tropicalization of an algebraic curve whose non-archimedean skeleton is
    faithfully represented by $Γ$. We give an affirmative answer to this question
    for a large class of tropical curves that includes all trivalent tropical curves,
    but also many tropical curves of higher valence. We then deduce that for every
    metric graph $G$ with rational edge lengths there exists a smooth algebraic curve
    in a toric variety whose analytification has skeleton $G$, and the corresponding
    tropicalization is faithful. Our approach is based on a combination of the theory
    of toric schemes over discrete valuation rings and logarithmically smooth deformation
    theory, expanding on a framework introduced by Nishinou and Siebert.
author:
- first_name: Man-Wai
  full_name: Cheung, Man-Wai
  last_name: Cheung
- first_name: Lorenzo
  full_name: Fantini, Lorenzo
  last_name: Fantini
- first_name: Jennifer
  full_name: Park, Jennifer
  last_name: Park
- first_name: Martin
  full_name: Ulirsch, Martin
  last_name: Ulirsch
citation:
  ama: Cheung M-W, Fantini L, Park J, Ulirsch M. Faithful realizability of tropical
    curves. <i>arXiv:14104152</i>. Published online 2014.
  apa: Cheung, M.-W., Fantini, L., Park, J., &#38; Ulirsch, M. (2014). Faithful realizability
    of tropical curves. <i>ArXiv:1410.4152</i>.
  bibtex: '@article{Cheung_Fantini_Park_Ulirsch_2014, title={Faithful realizability
    of tropical curves}, journal={arXiv:1410.4152}, author={Cheung, Man-Wai and Fantini,
    Lorenzo and Park, Jennifer and Ulirsch, Martin}, year={2014} }'
  chicago: Cheung, Man-Wai, Lorenzo Fantini, Jennifer Park, and Martin Ulirsch. “Faithful
    Realizability of Tropical Curves.” <i>ArXiv:1410.4152</i>, 2014.
  ieee: M.-W. Cheung, L. Fantini, J. Park, and M. Ulirsch, “Faithful realizability
    of tropical curves,” <i>arXiv:1410.4152</i>, 2014.
  mla: Cheung, Man-Wai, et al. “Faithful Realizability of Tropical Curves.” <i>ArXiv:1410.4152</i>,
    2014.
  short: M.-W. Cheung, L. Fantini, J. Park, M. Ulirsch, ArXiv:1410.4152 (2014).
date_created: 2026-07-08T07:22:48Z
date_updated: 2026-07-08T07:23:19Z
external_id:
  arxiv:
  - '1410.4152'
language:
- iso: eng
publication: arXiv:1410.4152
status: public
title: Faithful realizability of tropical curves
type: journal_article
user_id: '82981'
year: '2014'
...