Universality for tropical and logarithmic maps
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914603107090432 |
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| 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 |