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In 1969, P. Deligne and D. Mumford compactified the modulispace of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alt...
We define the dimension 2g − 1 Faber-Hurwitz Chow/homology classes on the moduli space of curves, parametrizing curves expressible as branched covers of P 1 with given ramification...
The moduli space of curves has proven itself a central object in geometry. The past decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, fro...
One relevant example (Example 4.9) turns out to be a proper integral variety with no embeddings in a smooth algebraic space. This one-paragraph construction appears to be simpler and more elementary...
We speculate about an algebro-geometric proof of Harer’s theorem on the rational Picard group of the moduli space of smooth complex curves. In particular, we refine the approach of Diaz and Edidin in-...
The universal theta divisor over the moduli space Ag of principally polarized abelian varieties of dimension g, is the divisor g inside the universal abelian variety Xg over Ag.
We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satis es a topological recursion formu...

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