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arXiv · 2211.15719

Universality for tropical and logarithmic maps

Gabriel Corrigan·Navid Nabijou·Dan Simms
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Abstract

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.

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Gabriel Corrigan, Navid Nabijou, Dan Simms. 2022-11-28. Universality for tropical and logarithmic maps. https://doi.org/10.46298/epiga.2024.12349

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