Acta Mathematica

The κ ring of the moduli of curves of compact type

Rahul Pandharipande

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The subalgebra of the tautological ring of the moduli of curves of compact type generated by the κ 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 κ rings are computed. A universality property relating the higher genus κ rings to the genus 0 rings is proven using the virtual geometry of the moduli space of stable maps. The λg-formula for Hodge integrals arises as the simplest consequence.

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Acta Math., Volume 208, Number 2 (2012), 335-388.

Received: 24 January 2010
Revised: 15 July 2011
First available in Project Euclid: 31 January 2017

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2012 © Institut Mittag-Leffler


Pandharipande, Rahul. The κ ring of the moduli of curves of compact type. Acta Math. 208 (2012), no. 2, 335--388. doi:10.1007/s11511-012-0078-2.

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