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.
Download full text files
Additional Services
| Author: | Andreas GrossGND, Martin UlirschORCiDGND, Dmitry ZakharovORCiD |
|---|---|
| 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 |
