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

Dimitri Zvonkine
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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.

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BibTeXRIS

Dimitri Zvonkine. 2003-04-18. Counting ramified coverings and intersection theory on Hurwitz spaces II (Local structure of Hurwitz spaces and combinatorial results). https://arxiv.org/abs/math/0304251

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