Principal bundles on metric graphs: the $\mathrm{GL}_n$ case

Autor:	Gross, Andreas, Ulirsch, Martin, Zakharov, Dmitry
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry 14T20 14H60
Druh dokumentu:	Working Paper
Popis:	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. Comment: 31 pages. Comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.10219 Zobrazit plný text záznamu View this record from Arxiv