Pixton's double ramification cycle relations

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.

40 pages. v2: Correction to proof of Lemma 4.2; results of Section 4 assume that exactly one a_i is negative, and the general case is deduced by polynomiality in A. v3: Substantial changes to Section 6 and the Appendix

References in corpus (3)

• Double ramification cycles on the moduli spaces of curves
• Virasoro Constraints for Toric Bundles
• Geometry of theta divisors --- a survey

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• Topological recursion relations from Pixton's formula
• A generalization of Witten's conjecture for the Pixton class and the noncommutative KdV hierarchy
• Tropical double ramification loci
• The tautological ring of ${\overline{\mathcal{M}}}_{g,n}$ is rarely Gorenstein
• Structures in topological recursion relations