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Relations in the tautological ring of $M_g$

Eleny-Nicoleta Ionel
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Abstract

Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of $M_g$ (and in fact that of $M_{g,2}$). One immediate consequence of these relations is that the classes $κ_1,...,κ_{[g/3]}$ generate the tautological ring of $M_g$, which has been conjectured by Faber, and recently proven at the level of {\em cohomology} by Morita.

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Eleny-Nicoleta Ionel. 2003-12-04. Relations in the tautological ring of $M_g$. https://arxiv.org/abs/math/0312100

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