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Tropicalization of the universal Jacobian
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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.Comment: 51 pages, 2 figures, v3: published version
Centre pour la Communication Scientifique Directe (CCSD)
Title: Tropicalization of the universal Jacobian
Description:
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.
Comment: 51 pages, 2 figures, v3: published version.
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