Principal bundles on metric graphs: the GLn case
- 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.
Author: | Andreas GrossGND, Martin UlirschORCiDGND, Dmitry ZakharovORCiD |
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URN: | urn:nbn:de:hebis:30:3-792221 |
DOI: | https://doi.org/10.48550/arXiv.2206.10219 |
ArXiv Id: | http://arxiv.org/abs/2206.10219v1 |
Parent Title (German): | ArXiv |
Publisher: | arXiv |
Document Type: | Preprint |
Language: | English |
Date of Publication (online): | 2022/06/21 |
Date of first Publication: | 2022/06/21 |
Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
Release Date: | 2024/02/15 |
Issue: | 2206.10219 Version 1 |
Edition: | Version 1 |
Page Number: | 31 |
HeBIS-PPN: | 516147137 |
Institutes: | Informatik und Mathematik / Mathematik |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Hxx Curves / 14H60 Vector bundles on curves and their moduli [See also 14D20, 14F05] |
Sammlungen: | Universitätspublikationen |
Licence (German): | Creative Commons - CC BY - Namensnennung 4.0 International |