Geodesic
Tropicalization of the universal Jacobian
Épijournal de Géométrie Algébrique, Tome 6 (2022)

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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.
DOI : 10.46298/epiga.2022.8352
Classification : 14A21, 14H10, 14H40, 14T15, 14T20 
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     author = {Melo, Margarida and Molcho, Samouil and Ulirsch, Martin and Viviani, Filippo},
     title = {Tropicalization of the universal {Jacobian}},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {6},
     year = {2022},
     doi = {10.46298/epiga.2022.8352},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.8352/}
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Melo, Margarida; Molcho, Samouil; Ulirsch, Martin; Viviani, Filippo. Tropicalization of the universal Jacobian. Épijournal de Géométrie Algébrique, Tome 6 (2022). doi: 10.46298/epiga.2022.8352

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