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Rahul Pandharipande - Stable quotients and relations in the tautological ring


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Rahul Pandharipande - Stable quotients and relations in the tautological ring

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
nal result establishes a previously conjectural set of tautological relations proposed a decade ago by
Faber{Zagier.
 

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