Geodesic
Universality for tropical and logarithmic maps
Épijournal de Géométrie Algébrique, Tome 8 (2024)

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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.
DOI : 10.46298/epiga.2024.12349
Classification : 14A21, 14H10, 14M25, 14N35, 14T20 
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     title = {Universality for tropical and logarithmic maps},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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Corrigan, Gabriel; Nabijou, Navid; Simms, Dan. Universality for tropical and logarithmic maps. Épijournal de Géométrie Algébrique, Tome 8 (2024). doi: 10.46298/epiga.2024.12349

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