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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67127The 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.39 pages, 1 figureAlgebraic GeometryCombinatoricsCounting ramified coverings and intersection theory on Hurwitz spaces II (Local structure of Hurwitz spaces and combinatorial results)text