Socle pairings on tautological rings

Felix Janda; Aaron Pixton

Socle pairings on tautological rings

Research output: Contribution to journal › Article › peer-review

Abstract

We study some aspects of the λ_g-pairing on the tautological ring of M_g ^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 λ_gλ_g ₋₁-pairing on the tautological ring of M_g.

Original language	English (US)
Article number	30
Journal	Epijournal de Geometrie Algebrique
Volume	3
State	Published - 2019
Externally published	Yes

Keywords

Gorenstein conjecture
Kappa ring
Moduli of curves
Tautological ring

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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title = "Socle pairings on tautological rings",

abstract = "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.",

keywords = "Gorenstein conjecture, Kappa ring, Moduli of curves, Tautological ring",

author = "Felix Janda and Aaron Pixton",

note = "Funding Information: The first named author was supported by the Swiss National Science Foundation grant SNF 200021_143274. The second named author was supported by an NDSEG graduate fellowship. Publisher Copyright: {\textcopyright} by the author(s)",

year = "2019",

language = "English (US)",

volume = "3",

journal = "Epijournal de Geometrie Algebrique",

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T1 - Socle pairings on tautological rings

AU - Janda, Felix

AU - Pixton, Aaron

N1 - Funding Information: The first named author was supported by the Swiss National Science Foundation grant SNF 200021_143274. The second named author was supported by an NDSEG graduate fellowship. Publisher Copyright: © by the author(s)

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Gorenstein conjecture

KW - Kappa ring

KW - Moduli of curves

KW - Tautological ring

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JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

M1 - 30

ER -

Socle pairings on tautological rings

Abstract

Keywords

ASJC Scopus subject areas

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