{"date_updated":"2026-07-08T09:35:05Z","year":"2022","title":"Principal bundles on metric graphs: the $\\mathrm{GL}_n$ case","status":"public","author":[{"last_name":"Gross","first_name":"Andreas","full_name":"Gross, Andreas"},{"id":"114697","last_name":"Ulirsch","first_name":"Martin","full_name":"Ulirsch, Martin"},{"first_name":"Dmitry","last_name":"Zakharov","full_name":"Zakharov, Dmitry"}],"user_id":"82981","doi":"10.1016/j.aim.2022.108775","language":[{"iso":"eng"}],"_id":"66316","abstract":[{"text":"Using the notion of a root datum of a reductive group $G$ we propose a tropical analogue of a principal $G$-bundle on a metric graph. We focus on the case $G=\\mathrm{GL}_n$, i.e. the case of vector bundles. Here we give a characterization of vector bundles in terms of multidivisors and use this description to prove analogues of the Weil--Riemann--Roch theorem and the Narasimhan--Seshadri correspondence. We proceed by studying the process of tropicalization. In particular, we show that the non-Archimedean skeleton of the moduli space of semistable vector bundles on a Tate curve is isomorphic to a certain component of the moduli space of semistable tropical vector bundles on its dual metric graph.","lang":"eng"}],"publication":"arXiv:2206.10219","citation":{"apa":"Gross, A., Ulirsch, M., &#38; Zakharov, D. (2022). Principal bundles on metric graphs: the $\\mathrm{GL}_n$ case. <i>ArXiv:2206.10219</i>. <a href=\"https://doi.org/10.1016/j.aim.2022.108775\">https://doi.org/10.1016/j.aim.2022.108775</a>","ieee":"A. Gross, M. Ulirsch, and D. Zakharov, “Principal bundles on metric graphs: the $\\mathrm{GL}_n$ case,” <i>arXiv:2206.10219</i>, 2022, doi: <a href=\"https://doi.org/10.1016/j.aim.2022.108775\">10.1016/j.aim.2022.108775</a>.","short":"A. Gross, M. Ulirsch, D. Zakharov, ArXiv:2206.10219 (2022).","chicago":"Gross, Andreas, Martin Ulirsch, and Dmitry Zakharov. “Principal Bundles on Metric Graphs: The $\\mathrm{GL}_n$ Case.” <i>ArXiv:2206.10219</i>, 2022. <a href=\"https://doi.org/10.1016/j.aim.2022.108775\">https://doi.org/10.1016/j.aim.2022.108775</a>.","mla":"Gross, Andreas, et al. “Principal Bundles on Metric Graphs: The $\\mathrm{GL}_n$ Case.” <i>ArXiv:2206.10219</i>, 2022, doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108775\">10.1016/j.aim.2022.108775</a>.","ama":"Gross A, Ulirsch M, Zakharov D. Principal bundles on metric graphs: the $\\mathrm{GL}_n$ case. <i>arXiv:220610219</i>. Published online 2022. doi:<a href=\"https://doi.org/10.1016/j.aim.2022.108775\">10.1016/j.aim.2022.108775</a>","bibtex":"@article{Gross_Ulirsch_Zakharov_2022, title={Principal bundles on metric graphs: the $\\mathrm{GL}_n$ case}, DOI={<a href=\"https://doi.org/10.1016/j.aim.2022.108775\">10.1016/j.aim.2022.108775</a>}, journal={arXiv:2206.10219}, author={Gross, Andreas and Ulirsch, Martin and Zakharov, Dmitry}, year={2022} }"},"type":"journal_article","external_id":{"arxiv":["2206.10219"]},"date_created":"2026-07-08T06:42:43Z"}