Geometry of meromorphic functions and intersections on moduli spaces of curves

Details Geometry of meromorphic functions and intersections on moduli spaces of curves Geometry of meromorphic functions and intersections on moduli spaces of curves

2002-09-21

arxiv.org/abs/math/0209282v2

Int. Math. Res. Not. 2003, no. 38, 2051-2094

Mathematics

Algebraic Geometry

38 pages

Scientific paper

10.1155/S1073792803212101

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.

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