TY  - INPR
A1  - Gross, Andreas
A1  - Ulirsch, Martin
A1  - Zakharov, Dmitry
T1  - Principal bundles on metric graphs: the GLn case
T2  - ArXiv
N2  - 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=GLn, 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.
Y1  - 2022
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/79222
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-792221
IS  - 2206.10219 Version 1
PB  - arXiv
ER  -