Stable quotients and relations in the tautological ring
Appears in collection : Summer School 2011 - MODULES DE COURBES ET THEORIE DE GROMOV-WITTEN
The topic concerns relations among the kappa classes in the tautological ring of the moduli space of genus g curves. After a discussion of classical constructions in Wick form, we derive an explicit set of relations obtained from the virtual geometry of the moduli space of stable quotients. In a series of steps, the stable quotient relations are transformed to simpler and simpler forms. Our final result establishes a previously conjectural set of tautological relations proposed a decade ago by Faber-Zagier.
