Computing top intersections in the tautological ring of $M_g$

TL;DR

This paper develops recursion formulas for calculating top intersections in the tautological ring of the moduli space of curves, leading to new tautological relations in algebraic geometry.

Contribution

It introduces effective recursion formulas for top intersections in the tautological ring of $M_g$, and proves a new tautological relation in $R^{g-2}(M_g)$.

Findings

Derived explicit recursion formulas for top intersections

Established a convolution-type tautological relation

Enhanced understanding of the structure of $R^*(M_g)$

Abstract

We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.