Tropical pseudostable curves
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911826237718528 |
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| author | Cavalieri, Renzo Marcus, Steffen Wise, Jonathan |
| author_facet | Cavalieri, Renzo Marcus, Steffen Wise, Jonathan |
| contents | We study the tropical version of the contraction morphism $\mathcal{T}$ between moduli spaces of stable and pseudostable curves. By promoting $\mathcal{T}$ to a logarithmic morphism, we obtain a piecewise linear function between the generalized cone complexes parameterizing tropical stable and pseudostable curves. The ray corresponding to the contracted divisor $δ_1$ is not contracted to the cone point but mapped onto a ray of $\mathcal{M}_{g,n}^{{\rm trop}, {\rm ps}}$, with a slope reflecting the geometry of the desingularization of a plane cusp. We explore in detail the situation of $g=1$, where the tautological geometry of both spaces is fully described by piecewise polynomial functions on the tropical moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical pseudostable curves Cavalieri, Renzo Marcus, Steffen Wise, Jonathan Algebraic Geometry 14H10, 14T20 We study the tropical version of the contraction morphism $\mathcal{T}$ between moduli spaces of stable and pseudostable curves. By promoting $\mathcal{T}$ to a logarithmic morphism, we obtain a piecewise linear function between the generalized cone complexes parameterizing tropical stable and pseudostable curves. The ray corresponding to the contracted divisor $δ_1$ is not contracted to the cone point but mapped onto a ray of $\mathcal{M}_{g,n}^{{\rm trop}, {\rm ps}}$, with a slope reflecting the geometry of the desingularization of a plane cusp. We explore in detail the situation of $g=1$, where the tautological geometry of both spaces is fully described by piecewise polynomial functions on the tropical moduli spaces. |
| title | Tropical pseudostable curves |
| topic | Algebraic Geometry 14H10, 14T20 |
| url | https://arxiv.org/abs/2404.02654 |