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The tautological ring of the moduli space of stable curves

4:00 pm Thursday, December 05, 2013
Aaron Pixton (Princeton University)

The tautological ring of the moduli space of smooth curves of genus g is the subring of its Chow ring generated by the kappa classes. This subring was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of the tautological ring. After reviewing these conjectures, I will discuss how the situation changes when the moduli space of smooth curves is replaced by its compactification, the moduli space of Deligne-Mumford stable curves.

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