Universality for tropical and logarithmic maps

Fuente: arXiv
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Main Authors: Corrigan, Gabriel, Nabijou, Navid, Simms, Dan
Format: Preprint
Published: 2022
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_version_ 1866914603107090432
author Corrigan, Gabriel
Nabijou, Navid
Simms, Dan
author_facet Corrigan, Gabriel
Nabijou, Navid
Simms, Dan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2211_15719
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Universality for tropical and logarithmic maps
Corrigan, Gabriel
Nabijou, Navid
Simms, Dan
Algebraic Geometry
Combinatorics
14N35, 14H10, 14T20, 14A21, 14M25
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.
title Universality for tropical and logarithmic maps
topic Algebraic Geometry
Combinatorics
14N35, 14H10, 14T20, 14A21, 14M25
url https://arxiv.org/abs/2211.15719