---
_id: '66322'
abstract:
- lang: eng
  text: 'Motivated by the realizability problem for principal tropical divisors with
    a fixed ramification profile, we explore the tropical geometry of the double ramification
    locus in $\mathcal{M}_{g,n}$.There are two ways to define a tropical analogue
    of the double ramification locus: one as a locus of principal divisors, the other
    as a locus of finite effective ramified covers of a tree. We show that both loci
    admit a structure of a generalized cone complex in $M_{g,n}^{trop}$, with the
    latter contained in the former. We prove that the locus of principal divisors
    has cones of codimension zero in $M_{g,n}^{trop}$, while the locus of ramified
    covers has the expected codimension $g$. This solves the deformation-theoretic
    part of the realizability problem for principal divisors, reducing it to the so-called
    Hurwitz existence problem for covers of a fixed ramification type.'
author:
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Dmitry
  full_name: Zakharov, Dmitry
  last_name: Zakharov
citation:
  ama: Ulirsch M, Zakharov D. Tropical double ramification loci. <i>arXiv:191001499</i>.
    Published online 2019.
  apa: Ulirsch, M., &#38; Zakharov, D. (2019). Tropical double ramification loci.
    In <i>arXiv:1910.01499</i>.
  bibtex: '@article{Ulirsch_Zakharov_2019, title={Tropical double ramification loci},
    journal={arXiv:1910.01499}, author={Ulirsch, Martin and Zakharov, Dmitry}, year={2019}
    }'
  chicago: Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.”
    <i>ArXiv:1910.01499</i>, 2019.
  ieee: M. Ulirsch and D. Zakharov, “Tropical double ramification loci,” <i>arXiv:1910.01499</i>.
    2019.
  mla: Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.”
    <i>ArXiv:1910.01499</i>, 2019.
  short: M. Ulirsch, D. Zakharov, ArXiv:1910.01499 (2019).
date_created: 2026-07-08T06:49:12Z
date_updated: 2026-07-08T06:49:19Z
external_id:
  arxiv:
  - '1910.01499'
language:
- iso: eng
publication: arXiv:1910.01499
status: public
title: Tropical double ramification loci
type: preprint
user_id: '82981'
year: '2019'
...