Relations in the tautological ring of ℳ g

Abstract

Using a simple geometric argument, we obtain an infinite family of nontrivial relations in the tautological ring of ${ℳ}_g$ (coming, in fact, from relations in the Chow ring of ${\overline{ℳ}}_{g,2}$). One immediate consequence of these relations is that the classes ${\kappa }_1,\dots ,{\kappa }_{\left[g/3\right]}$ generate the tautological ring of ${ℳ}_g$, which was conjectured by Faber in [F] and recently proven at the level of cohomology by Morita in [M].