Recursion formulae of higher Weil-Petersson volumes

Abstract

In this paper we study effective recursion formulae for computing intersection numbers of mixed $\psi$ and $\kappa$ classes on moduli spaces of curves. By using the celebrated Witten-Kontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani's recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the tautological rings of moduli spaces of curves.

18 pages, to appear in IMRN

References in corpus (3)

• Virasoro constraints and the Chern classes of the Hodge bundle
• Estimates of Weil-Petersson volumes via effective divisors
• Intersection Numbers and Rank One Cohomological Field Theories in Genus One

Cited by in corpus (4)

• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• A high-genus asymptotic expansion of Weil-Petersson volume polynomials
• Cut-and-join operators for higher Weil-Petersson volumes
• On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus