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AN ANALYTIC CONSTRUCTION OF THE DELIGNE-MUMFORD COMPACTIFICATION OF THE MODULI SPACE OF CURVES
ANALYTIC CONSTRUCTION DELIGNE-MUMFORD COMPACTIFICATION MODULI SPACE OF CURVES
2015/8/26
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...
THE MODULI SPACE OF CURVES, DOUBLE HURWITZ NUMBERS, AND FABER’S INTERSECTION NUMBER CONJECTURE
DOUBLE HURWITZ NUMBERS FABER’S INTERSECTION NUMBER CONJECTURE
2015/7/14
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...
THE AFFINE STRATIFICATION NUMBER AND THE MODULI SPACE OF CURVES
AFFINE STRATIFICATION NUMBER MODULI SPACE
2015/7/14
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...
As an illustration, we describe a new approach to Faber’s intersection number
conjecture via branched covers of the projective line (work with I.P. Goulden and D.M.
Jackson, based on work with T. Gr...
On the rational Picard group of the moduli space of curves
rational Picard group moduli space of curves
2011/2/25
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 of curves
universal theta divisor moduli space of curves
2010/11/26
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.
Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves
Topological recursion Poincare polynomial combinatorial moduli space of curves
2010/12/3
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...