Relations on M_g,n via equivariant Gromov-Witten theory of \mathbb P¹

2015/09/30 by Felix Janda
Mathematics · #math.AG

paper · pdf · doi:10.14231/ag-2017-018

published as Algebraic Geometry (Foundation Compositio Mathematica), 4 (3): 311-336 (May 2017) · 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

arxiv created 2017/07/28 · arxiv updated 2021/03/30

Abstract

We give a proof of Pixton's generalized Faber-Zagier relations in the tautological Chow ring of 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.

Citations

• Tautological relations in moduli spaces of weighted pointed curves
• Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures