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 $M_g$ (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.

24 pages

References in corpus (1)

• On the tautological ring of $\M _g$

Cited by in corpus (5)

• Relations in the tautological ring of the moduli space of curves
• Tautological relations in moduli spaces of weighted pointed curves
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures
• Computing top intersections in the tautological ring of $M_g$