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Tropical Hurwitz spaces

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 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. / text

Identiferoai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2011-12-4777
Date01 February 2012
CreatorsKatz, Brian Paul
Source SetsUniversity of Texas
LanguageEnglish
Detected LanguageEnglish
Typethesis
Formatapplication/pdf

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