The Tropical Moduli Space of Degree-3 Rational Maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909044388659200 |
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| author | Shaska, Tony Siadat, Mohammad-Reza |
| author_facet | Shaska, Tony Siadat, Mohammad-Reza |
| contents | We construct and study the tropical moduli space \(\mathcal{M}_3^{\mathrm{trop}}\) of degree-$3$ tropical rational maps \(\mathbb{T}\PP^1 \to \mathbb{T}\PP^1\) up to post-composition. Using a combinatorial description in terms of slope sequences, we classify all such maps and show that there are exactly ten combinatorial types. This yields a polyhedral model of \(\mathcal{M}_3^{\mathrm{trop}}\) parametrized by gap lengths between break points.
We determine the automorphism groups and obtain a stratification by explicit linear conditions. We also relate the construction to tropical Hurwitz theory and describe a natural compactification via degenerations of the parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Tropical Moduli Space of Degree-3 Rational Maps Shaska, Tony Siadat, Mohammad-Reza Algebraic Geometry Combinatorics 14T05, 14D22, 14H10 G.2.1; I.2.6 We construct and study the tropical moduli space \(\mathcal{M}_3^{\mathrm{trop}}\) of degree-$3$ tropical rational maps \(\mathbb{T}\PP^1 \to \mathbb{T}\PP^1\) up to post-composition. Using a combinatorial description in terms of slope sequences, we classify all such maps and show that there are exactly ten combinatorial types. This yields a polyhedral model of \(\mathcal{M}_3^{\mathrm{trop}}\) parametrized by gap lengths between break points. We determine the automorphism groups and obtain a stratification by explicit linear conditions. We also relate the construction to tropical Hurwitz theory and describe a natural compactification via degenerations of the parameters. |
| title | The Tropical Moduli Space of Degree-3 Rational Maps |
| topic | Algebraic Geometry Combinatorics 14T05, 14D22, 14H10 G.2.1; I.2.6 |
| url | https://arxiv.org/abs/2605.15347 |