Generalized boundary strata classes

TL;DR

This paper introduces a generalized class of boundary strata in the Chow ring of moduli spaces of curves, forming a subring that includes all double ramification cycles, with a new multiplication law.

Contribution

It generalizes boundary strata classes to form a subring of the tautological ring and establishes a multiplication law for these classes.

Findings

Double ramification cycles are contained in the subring.

The generalized classes span a subring of the tautological ring.

A multiplication law for these classes is described.

Abstract

We describe a generalization of the usual boundary strata classes in the Chow ring of $\overline{\mathcal{M}}_{g,n}$. The generalized boundary strata classes additively span a subring of the tautological ring. We describe a multiplication law satisfied by these classes and check that every double ramification cycle lies in this subring.