Tropical pseudostable curves

Fuente: arXiv
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Autori principali: Cavalieri, Renzo, Marcus, Steffen, Wise, Jonathan
Natura: Preprint
Pubblicazione: 2024
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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