Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$

Abstract

We give a proof of Pixton's generalized Faber-Zagier relations in the tautological Chow ring of ${\overline{M}}_{g,n}$. The strategy is very similar to the work of Pandharipande-Pixton-Zvonkine, who have given a proof of the same result in cohomology. The main tool is the Givental-Teleman classification of semisimple cohomological field theories, which, while in general only known in cohomology, via virtual localization can be shown to be also valid in Chow for the equivariant Gromov-Witten theory of the projective line. We obtain the relations just from this theory.

29 pages. Supersedes proof of arXiv:1306.6580. Appendix taken from arXiv:1407.4778, v2: many improvements from referee's comments, v3: agrees with published version

References in corpus (3)

• Conjectural relations in the tautological ring of ${\bar{M}}_{g,n}$
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• A calculus for the moduli space of curves

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• Cohomological field theories with non-tautological classes
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• The tautological ring of ${\overline{\mathcal{M}}}_{g,n}$ is rarely Gorenstein