Recursion between Mumford volumes of moduli spaces

Bertrand Eynard (1)

1 SPhT - Service de Physique Théorique

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.

Mots clés: moduli spaces; mumford classes; mirzakhani; kontsevich; matrix; recursion; intersection

Domaines: Géométrie algébrique [math.AG]; Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Bertrand Eynard. Recursion between Mumford volumes of moduli spaces. 2007. ⟨hal-00158738⟩