TY  - INPR
A1  - Melo, Margarida
A1  - Molcho, Samouil
A1  - Ulirsch, Martin
A1  - Viviani, Filippo
T1  - Tropicalization of the universal Jacobian
T2  - arXiv
N2  - 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.
KW  - universal compactified Jacobian
KW  - tropical universal Jacobian
KW  - tropicalization
KW  - tropical geometry
KW  - logarithmic geometry
KW  - non-archimedean geometry
Y1  - 2022
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/81811
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-818115
IS  - 2108.04711 Version 3
PB  - arXiv
ER  -