The Kontsevich constants for the volume of the moduli of curves and topological recursion

Details The Kontsevich constants for the volume of the moduli of curves and topological recursion The Kontsevich constants for the volume of the moduli of curves and topological recursion

2010-09-10

arxiv.org/abs/1009.2055v3

Mathematics

Algebraic Geometry

37 pages with 20 figures

Scientific paper

We give an Eynard-Orantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edge removal operation on the space of ribbon graphs. As an application we obtain a new proof of the Kontsevich constants for the ratio of the Euclidean and the symplectic volumes of the moduli space of curves.

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