Duke Mathematical Journal

Relations in the tautological ring of $\mathcal{M}_g$

Eleny-Nicoleta Ionel

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Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of $\mathcal{M}_g$ (coming, in fact, from relations in the Chow ring of $\overline{\mathcal{M}}_{g,2}$). One immediate consequence of these relations is that the classes $\kappa_1,\ldots,\kappa_{[g/3]}$ generate the tautological ring of $\mathcal{M}_g$, which was conjectured by Faber in [F] and recently proven at the level of cohomology by Morita in [M].

Article information

Duke Math. J. Volume 129, Number 1 (2005), 157-186.

First available in Project Euclid: 15 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)


Ionel, Eleny-Nicoleta. Relations in the tautological ring of ℳ g . Duke Math. J. 129 (2005), no. 1, 157--186. doi:10.1215/S0012-7094-04-12916-1. http://projecteuclid.org/euclid.dmj/1121448867.

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