Socle pairings on tautological rings
Name
1304.0026.pdf
Description
Published version
Size
437.54 KB
Format
Adobe PDF
Checksum (MD5)
46c961ed4cb037dade82a1399a3e8eea
Author(s)
Janda, Felix
Pixton, Aaron
Date Issued
2019
Journal
Épijournal de Géométrie Algébrique
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Citation
Janda, Felix and Pixton, Aaron. 2019. "Socle pairings on tautological rings." Épijournal de Géométrie Algébrique, Volume 3.
Version
Final published version
Abstract
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 $M_g$.
$M_g^c$, 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 $M_g$.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-ShareAlike 4.0 International
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.46298/EPIGA.2019.VOLUME3.3784
