Tautological pairings on moduli spaces of curves
Renzo Cavalieri, Stephanie Yang
TL;DR
This paper investigates the structure of tautological rings on certain compactifications of the moduli space of smooth curves, revealing they are one-dimensional in top degree but lack Poincare duality.
Contribution
It introduces analogs of Faber's conjecture for new nested compactifications and analyzes their tautological rings' properties.
Findings
Tautological rings are one-dimensional in top degree.
These rings do not satisfy Poincare duality.
The work extends understanding of tautological structures on moduli spaces.
Abstract
We discuss analogs of Faber's conjecture for two nested sequences of partial compactifications of the moduli space of smooth curves. We show that their tautological rings are one-dimensional in top degree but do not satisfy Poincare duality.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology