Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures

2014/07/17 by Felix Janda, Janda, Felix · 1 citation
Mathematics · #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10

paper · pdf · doi:10.48550/arxiv.1407.4778

Part of author's PhD thesis, result superseded by arXiv:1505.03419, 31 pages; v3: Appendix rewritten, various corrections

arxiv created 2015/09/29 · arxiv updated 2015/09/30

Abstract

Pandharipande-Pixton-Zvonkine's proof of Pixton's generalized Faber-Zagier relations in the tautological ring of M_{g, n} has started the study of tautological relations from semisimple cohomological field theories. In this article we compare the relations obtained in the examples of the equivariant Gromov-Witten theory of projective spaces and of spin structures. We prove an equivalence between the \mathbb P¹- and 3-spin relations, and more generally between restricted \mathbb P^m-relations and similarly restricted (m + 2)-spin relations. We also show that the general \mathbb P^m-relations imply the (m + 2)-spin relations.

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

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