Relations in the tautological ring of $M_g$

Details Relations in the tautological ring of $M_g$ Relations in the tautological ring of $M_g$

2003-12-04

arxiv.org/abs/math/0312100v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

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 $\kappa_1,...,\kappa_{[g/3]}$ 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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