## Janda, Felix and Pixton, Aaron - Socle pairings on tautological rings

epiga:3784 - Épijournal de Géométrie Algébrique, April 2, 2019, Volume 3
Socle pairings on tautological rings

Authors: Janda, Felix and Pixton, Aaron

We study some aspects of the $\lambda_g$ pairing on the tautological ring of $M_g^c$, the moduli space of genus $g$ stable curves of compact type. We consider pairing kappa classes with pure boundary strata, all tautological classes supported on the boundary, or the full tautological ring. We prove that the rank of this restricted pairing is equal in the first two cases and has an explicit formula in terms of partitions, while in the last case the rank increases by precisely the rank of the $\lambda_g\lambda_{g - 1}$ pairing on the tautological ring of $M_g$.

Source : oai:arXiv.org:1304.0026
Volume: Volume 3
Published on: April 2, 2019
Submitted on: July 11, 2017
Keywords: Mathematics - Algebraic Geometry,14H10