The University of Michigan Combinatorics Seminar
Winter 2009
April 10, 4:10-5:00, 3866 East Hall



Universal polynomials for strata in Hurwitz spaces

Maxim Kazarian

Steklov Institute


Abstract

A Hurwitz space is a moduli spaces of meromorphic functions on complex curves. It is stratified according to the degeneration types of the critical values of the function. We compute explicitly the cohomology classes dual to the strata. These classes are represented in the form of universal expressions that are independent of the particular Hurwitz space, but completely determined by the local singularity type of critical values. The results are obtained by extending the theory of Thom polynomials of singularities and its multisingularity version to the to the case of maps with nonisolated singularities. The obtained expression contain all enumerative data related to the strata. In this way, we derive new closed expressions for a number of particular series of Hurwitz numbers.