Geometry of meromorphic functions and intersections on moduli spaces of curves

Abstract

In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, how intersection numbers can be expressed via Hurwitz numbers. And then we obtain an algorithm expressing intersection numbers $<\tau_{n,m}\prod_{i=0}^{r-1}\tau_{0,i}^{k_i}>_g$ via correlation functions of primaries.