---
_id: '66333'
abstract:
- lang: eng
  text: We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller on compactifications
    of strata of abelian differentials to give a comprehensive solution to the realizability
    problem for effective tropical canonical divisors in equicharacteristic zero.
    Given a pair $(Γ, D)$ consisting of a stable tropical curve $Γ$ and a divisor
    $D$ in the canonical linear system on $Γ$, we give a purely combinatorial condition
    to decide whether there is a smooth curve $X$ over a non-Archimedean field whose
    stable reduction has $Γ$ as its dual tropical curve together with a effective
    canonical divisor $K_X$ that specializes to $D$. Along the way, we develop a moduli-theoretic
    framework to understand Baker's specialization of divisors from algebraic to tropical
    curves as a natural toroidal tropicalization map in the sense of Abramovich-Caporaso-Payne.
author:
- first_name: Martin
  full_name: Moeller, Martin
  last_name: Moeller
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Annette
  full_name: Werner, Annette
  last_name: Werner
citation:
  ama: Moeller M, Ulirsch M, Werner A. Realizability of tropical canonical divisors.
    <i>arXiv:171006401</i>. Published online 2017. doi:<a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>
  apa: Moeller, M., Ulirsch, M., &#38; Werner, A. (2017). Realizability of tropical
    canonical divisors. <i>ArXiv:1710.06401</i>. <a href="https://doi.org/10.4171/JEMS/1009">https://doi.org/10.4171/JEMS/1009</a>
  bibtex: '@article{Moeller_Ulirsch_Werner_2017, title={Realizability of tropical
    canonical divisors}, DOI={<a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>},
    journal={arXiv:1710.06401}, author={Moeller, Martin and Ulirsch, Martin and Werner,
    Annette}, year={2017} }'
  chicago: Moeller, Martin, Martin Ulirsch, and Annette Werner. “Realizability of
    Tropical Canonical Divisors.” <i>ArXiv:1710.06401</i>, 2017. <a href="https://doi.org/10.4171/JEMS/1009">https://doi.org/10.4171/JEMS/1009</a>.
  ieee: 'M. Moeller, M. Ulirsch, and A. Werner, “Realizability of tropical canonical
    divisors,” <i>arXiv:1710.06401</i>, 2017, doi: <a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>.'
  mla: Moeller, Martin, et al. “Realizability of Tropical Canonical Divisors.” <i>ArXiv:1710.06401</i>,
    2017, doi:<a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>.
  short: M. Moeller, M. Ulirsch, A. Werner, ArXiv:1710.06401 (2017).
date_created: 2026-07-08T07:06:32Z
date_updated: 2026-07-08T09:40:36Z
doi: 10.4171/JEMS/1009
external_id:
  arxiv:
  - '1710.06401'
language:
- iso: eng
publication: arXiv:1710.06401
status: public
title: Realizability of tropical canonical divisors
type: journal_article
user_id: '82981'
year: '2017'
...