Socle pairings on tautological rings

Felix Janda, Aaron Pixton

Research output: Contribution to journalArticlepeer-review


We study some aspects of the λg-pairing on the tautological ring of Mg c, the moduli space of genus g stable curves of compact type. We consider pairing κ-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 λgλg −1-pairing on the tautological ring of Mg.

Original languageEnglish (US)
Article number30
JournalEpijournal de Geometrie Algebrique
StatePublished - 2019
Externally publishedYes


  • Gorenstein conjecture
  • Kappa ring
  • Moduli of curves
  • Tautological ring

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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