Recursion formulae of higher Weil-Petersson volumes

TL;DR

This paper develops new recursion formulas for calculating intersection numbers and higher Weil-Petersson volumes on moduli spaces of curves, generalizing previous results using the Witten-Kontsevich theorem.

Contribution

It introduces generalized recursion formulas for higher Weil-Petersson volumes and intersection pairings, expanding computational tools in the geometry of moduli spaces.

Findings

Derived a recursion formula for higher Weil-Petersson volumes.

Extended Mirzakhani's recursion to more general intersection numbers.

Provided explicit recursion formulas for tautological ring pairings.

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.