Relations on Mbar_{g,n} via orbifold stable maps

TL;DR

This paper derives new tautological relations on the moduli space of stable curves by analyzing orbifold stable maps and their associated virtual cycles, connecting geometric invariants with algebraic relations.

Contribution

It introduces a novel approach using equivariant virtual cycles and Chern class vanishing to establish relations in the Chow ring of moduli spaces.

Findings

Derived relations in the Chow ring of Mbar_{g,n}

Established connections between orbifold stable maps and tautological classes

Provided a new method for computing relations in moduli spaces

Abstract

Using the equivariant virtual cycle of the moduli space of stable maps to [C/Z_r], or equivalently, the vanishing of high-degree Chern classes of a certain vector bundle over the moduli space of stable maps to BZ_r, we derive relations in the Chow ring of Mbar_{g,n}(BZ_r,0). These push forward to yield tautological relations on Mbar_{g,n}.