Recursion between Mumford volumes of moduli spaces
Algebraic Geometry
2007-07-10 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0706.4403,
title = {Recursion between Mumford volumes of moduli spaces},
author = {Bertrand Eynard},
journal= {arXiv preprint arXiv:0706.4403},
year = {2007}
}