Thom Polynomials for Maps of Curves with Isolated Singularities

Thom (residual) polynomials in characteristic classes are used in the analysis of the geometry of function spaces. They serve as a tool for describing the classes that are Poincaré dual to subvarieties of functions with singularities of prescribed types. We give explicit universal expressions for residual polynomials in spaces of functions on complex curves that have isolated singularities and multisingularities, in terms of few characteristic classes. These expressions lead to a partial description of a stratification of Hurwitz spaces.