The kappa ring of the moduli of curves of compact type: I

2009/06/15 by Pandharipande, R.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.2657

Abstract

The subalgebra of the tautological ring of the moduli of curves of compact type generated by the kappa classes is studied in all genera. Relations, constructed via the virtual geometry of the moduli of stable quotients, are used to obtain minimal sets of generators. Bases and Betti numbers of the kappa rings are computed. A universality property relating the higher genus kappa rings to the genus 0 rings is stated and proved in a sequel. The lambda_g formula for Hodge integrals arises as the simplest consequence.

Related

• The kappa ring of the moduli of curves of compact type: II
• Relations in the tautological ring of the moduli space of curves
• The kappa classes on the moduli spaces of curves
• Relations in the tautological ring
• On the structure of the kappa-ring