The tautological ring of the moduli space M_{2,n}^rt

TL;DR

This paper investigates the structure of the tautological ring of the moduli space of genus two curves with rational tails, providing explicit generators, relations, and proving it is Gorenstein.

Contribution

It offers an explicit description of the tautological ring for M_{2,n}^{rt} and establishes its Gorenstein property, advancing understanding of its algebraic structure.

Findings

The tautological ring is generated by explicit classes.

Relations among generators are explicitly described.

The algebra is proven to be Gorenstein.

Abstract

We study the tautological ring of the moduli space of stable n-pointed curves of genus two with rational tails. The algebra is described in terms of explicit generators and relations. It is proven that this algebra is Gorenstein.