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arxiv: 1211.2369 · v1 · pith:MFJ3QZPZnew · submitted 2012-11-11 · 🧮 math.AG

Tropical Hurwitz Spaces

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keywords spacehurwitztropicalcurvesmodulimorphismdegreemarked
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Hurwitz numbers are a weighted count of degree d ramified covers of curves with specified ramification profiles at marked points on the codomain curve. Isomorphism classes of these covers can be included as a dense open set in a moduli space, called a Hurwitz space. The Hurwitz space has a forgetful morphism to the moduli space of marked, stable curves, and the degree of this morphism encodes the Hurwitz numbers. Mikhalkin has constructed a moduli space of tropical marked, stable curves, and this space is a tropical variety. In this paper, I construct a tropical analogue of the Hurwitz space in the sense that it is a connected, polyhedral complex with a morphism to the tropical moduli space of curves such that the degree of the morphism encodes the Hurwitz numbers.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The Tropical Moduli Space of Degree-3 Rational Maps

    math.AG 2026-05 unverdicted novelty 7.0

    The authors classify all degree-3 tropical rational maps into exactly ten combinatorial types and build a polyhedral model of their moduli space parametrized by gap lengths between breakpoints.