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 Mosc. Math. J., 2007, Volume 7, Number 1, Pages 135–162 (Mi mmj274)

Counting ramified coverings and intersection theory on Hurwitz spaces. II. Local structure of Hurwitz spaces and combinatorial results

D. Zvonkine

Institut de Mathématiques de Jussieu

Abstract: The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these numbers belong to a very particular subalgebra of the algebra of power series.

Key words and phrases: Riemann surfaces, moduli space, ramified coverings, Lyashko–Looijenga map, Hurwitz space, Hurwitz numbers.

DOI: https://doi.org/10.17323/1609-4514-2007-7-1-135-162

Full text: http://www.ams.org/.../abst7-1-2007.html
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MSC: 05A, 14C, 14D22, 30F
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Citation: D. Zvonkine, “Counting ramified coverings and intersection theory on Hurwitz spaces. II. Local structure of Hurwitz spaces and combinatorial results”, Mosc. Math. J., 7:1 (2007), 135–162

Citation in format AMSBIB
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This publication is cited in the following articles:
1. M. E. Kazarian, S. K. Lando, “Thom Polynomials for Maps of Curves with Isolated Singularities”, Proc. Steklov Inst. Math., 258 (2007), 87–99
2. Shadrin S., Shapiro A., Vainshtein A., “Chamber behavior of double Hurwitz numbers in genus 0”, Adv. Math., 217:1 (2008), 79–96