---
_id: '66325'
abstract:
- lang: eng
  text: Let $\mathfrak{A}$ be a finite abelian group. In this article, we classify
    harmonic $\mathfrak{A}$-covers of a tropical curve $Γ$ (which allow dilation along
    edges and at vertices) in terms of the cohomology group of a suitably defined
    sheaf on $Γ$. We give a realizability criterion for harmonic $\mathfrak{A}$-covers
    by patching local monodromy data in an extended homology group on $Γ$. As an explicit
    example, we work out the case $\mathfrak{A}=\mathbb{Z}/p\mathbb{Z}$ and explain
    how realizability for such covers is related to the nowhere-zero flow problem
    from graph theory.
author:
- first_name: Yoav
  full_name: Len, Yoav
  last_name: Len
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Dmitry
  full_name: Zakharov, Dmitry
  last_name: Zakharov
citation:
  ama: Len Y, Ulirsch M, Zakharov D. Abelian tropical covers. <i>arXiv:190604215</i>.
    Published online 2019. doi:<a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>
  apa: Len, Y., Ulirsch, M., &#38; Zakharov, D. (2019). Abelian tropical covers. <i>ArXiv:1906.04215</i>.
    <a href="https://doi.org/10.1017/S0305004123000518">https://doi.org/10.1017/S0305004123000518</a>
  bibtex: '@article{Len_Ulirsch_Zakharov_2019, title={Abelian tropical covers}, DOI={<a
    href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>},
    journal={arXiv:1906.04215}, author={Len, Yoav and Ulirsch, Martin and Zakharov,
    Dmitry}, year={2019} }'
  chicago: Len, Yoav, Martin Ulirsch, and Dmitry Zakharov. “Abelian Tropical Covers.”
    <i>ArXiv:1906.04215</i>, 2019. <a href="https://doi.org/10.1017/S0305004123000518">https://doi.org/10.1017/S0305004123000518</a>.
  ieee: 'Y. Len, M. Ulirsch, and D. Zakharov, “Abelian tropical covers,” <i>arXiv:1906.04215</i>,
    2019, doi: <a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>.'
  mla: Len, Yoav, et al. “Abelian Tropical Covers.” <i>ArXiv:1906.04215</i>, 2019,
    doi:<a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a>.
  short: Y. Len, M. Ulirsch, D. Zakharov, ArXiv:1906.04215 (2019).
date_created: 2026-07-08T06:50:59Z
date_updated: 2026-07-08T08:22:44Z
doi: 10.1017/S0305004123000518
external_id:
  arxiv:
  - '1906.04215'
language:
- iso: eng
publication: arXiv:1906.04215
status: public
title: Abelian tropical covers
type: journal_article
user_id: '82981'
year: '2019'
...