Margarida Melo ; Samouil Molcho ; Martin Ulirsch ; Filippo Viviani - Tropicalization of the universal Jacobian

epiga:8352 - Épijournal de Géométrie Algébrique, August 22, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.8352
Tropicalization of the universal JacobianArticle

Authors: Margarida Melo ; Samouil Molcho ORCID; Martin Ulirsch ORCID; Filippo Viviani

    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.


    Volume: Volume 6
    Published on: August 22, 2022
    Accepted on: May 2, 2022
    Submitted on: August 11, 2021
    Keywords: Mathematics - Algebraic Geometry,14T05, 14H10, 14H40
    Funding:
      Source : OpenAIRE Graph
    • Audience of the Future; Code: 107520
    • Center for Mathematics, University of Coimbra; Funder: Fundação para a Ciência e a Tecnologia, I.P.; Code: UIDB/00324/2020
    • Moduli, Algebraic Cycles, and Invariants; Funder: European Commission; Code: 786580
    • Birational and non-archimedean geometries; Funder: European Commission; Code: 770922
    • Foundations and applications of tropical moduli theory; Funder: European Commission; Code: 793039

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