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Geometry of meromorphic functions and intersections on moduli spaces of curves. (English) Zbl 1070.14030
Summary: 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 numbers via correlation functions of primaries.

MSC:
14H10 Families, moduli of curves (algebraic)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
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