Pixton's double ramification cycle relations

TL;DR

This paper proves Pixton's conjecture that his formula for the double ramification cycle vanishes in high codimension, leading to new tautological relations in the moduli space of curves.

Contribution

It confirms Pixton's conjecture and connects the resulting relations to Pixton's 3-spin relations through localization techniques.

Findings

Pixton's formula vanishes in codimension > g

New tautological relations are derived in the Chow ring

Relations are obtained via localization on moduli spaces

Abstract

We prove a conjecture of Pixton, namely that his proposed formula for the double ramification cycle on Mbar_{g,n} vanishes in codimension beyond g. This yields a collection of tautological relations in the Chow ring of Mbar_{g,n}. We describe, furthermore, how these relations can be obtained from Pixton's 3-spin relations via localization on the moduli space of stable maps to an orbifold projective line.