Gabriel Corrigan ; Navid Nabijou ; Dan Simms - Universality for tropical and logarithmic maps

epiga:12349 - Épijournal de Géométrie Algébrique, September 17, 2024, Volume 8 - https://doi.org/10.46298/epiga.2024.12349
Universality for tropical and logarithmic mapsArticle

Authors: Gabriel Corrigan ; Navid Nabijou ; Dan Simms

    We prove that every toric monoid appears in a space of maps from tropical curves to an orthant. It follows that spaces of logarithmic maps to Artin fans exhibit arbitrary toric singularities: a virtual universality theorem for logarithmic maps to pairs. The target rank depends on the chosen singularity: we show that the cone over the 7-gon never appears in a space of maps to a rank 1 target. We obtain similar results for tropical maps to affine space.


    Volume: Volume 8
    Published on: September 17, 2024
    Accepted on: March 19, 2024
    Submitted on: September 29, 2023
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Combinatorics,14N35, 14H10, 14T20, 14A21, 14M25

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