Tropicalization of the universal Jacobian
- In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.
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| Author: | Margarida MeloORCiD, Samouil MolchoORCiD, Martin UlirschORCiDGND, Filippo VivianiORCiD |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-818115 |
| DOI: | https://doi.org/10.48550/arXiv.2108.04711 |
| ArXiv Id: | http://arxiv.org/abs/2108.04711v3 |
| Parent Title (German): | arXiv |
| Publisher: | arXiv |
| Document Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2022/08/19 |
| Date of first Publication: | 2022/08/19 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2024/02/15 |
| Tag: | logarithmic geometry; non-archimedean geometry; tropical geometry; tropical universal Jacobian; tropicalization; universal compactified Jacobian |
| Issue: | 2108.04711 Version 3 |
| Edition: | Version 3 |
| Page Number: | 51 |
| HeBIS-PPN: | 516147161 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Hxx Curves / 14H10 Families, moduli (algebraic) |
| 14-XX ALGEBRAIC GEOMETRY / 14Hxx Curves / 14H40 Jacobians, Prym varieties [See also 32G20] | |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International |
