Degrees of Cohomology Classes of Multisingularities in Hurwitz Spaces of Rational Functions

Abstract

Hurwitz spaces are spaces of meromorphic functions with prescribed orders of poles on curves of a given genus. In this article, we derive new formulas for the degrees of the strata of Hurwitz spaces of genus 0 corresponding to functions that have two degenerate critical values with prescribed partitions of multiplicities of the preimages. More precisely, one of the critical values has an arbitrary multiplicity of the preimages, while the other is the simplest degenerate critical value.