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Moscow Mathematical Journal, 2007, Volume 7, Number 1, Pages 135–162
DOI: https://doi.org/10.17323/1609-4514-2007-7-1-135-162 (Mi mmj274) 		 
This article is cited in 3 scientific papers (total in 3 papers)

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
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DOI: https://doi.org/10.17323/1609-4514-2007-7-1-135-162
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.
Received: April 12, 2006
Bibliographic databases:
MSC: 05A, 14C, 14D22, 30F
Language: English
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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\by D.~Zvonkine
\paper Counting ramified coverings and intersection theory on Hurwitz spaces. II.~Local structure of Hurwitz spaces and combinatorial results
\jour Mosc. Math.~J.
\yr 2007
\vol 7
\issue 1
\pages 135--162
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2324560}
\zmath{https://zbmath.org/?q=an:1131.14037}
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