[{"date_updated":"2026-07-08T08:22:44Z","title":"Abelian tropical covers","year":"2019","status":"public","author":[{"full_name":"Len, Yoav","last_name":"Len","first_name":"Yoav"},{"last_name":"Ulirsch","first_name":"Martin","full_name":"Ulirsch, Martin","id":"114697"},{"full_name":"Zakharov, Dmitry","first_name":"Dmitry","last_name":"Zakharov"}],"doi":"10.1017/S0305004123000518","user_id":"82981","language":[{"iso":"eng"}],"_id":"66325","abstract":[{"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.","lang":"eng"}],"publication":"arXiv:1906.04215","citation":{"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>.","short":"Y. Len, M. Ulirsch, D. Zakharov, ArXiv:1906.04215 (2019).","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>.","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} }","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>","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>."},"type":"journal_article","external_id":{"arxiv":["1906.04215"]},"date_created":"2026-07-08T06:50:59Z"}]