Recursion between Mumford volumes of moduli spaces

Details Recursion between Mumford volumes of moduli spaces Recursion between Mumford volumes of moduli spaces

2007-06-29

arxiv.org/abs/0706.4403v1

Mathematics

Algebraic Geometry

Latex, 18 pages

Scientific paper

We propose a new proof, as well as a generalization of Mirzakhani's recursion for volumes of moduli spaces. We interpret those recursion relations in terms of expectation values in Kontsevich's integral, i.e. we relate them to a Ribbon graph decomposition of Riemann surfaces. We find a generalization of Mirzakhani's recursions to measures containing all higher Mumford's kappa classes, and not only kappa1 as in the Weil-Petersson case.

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