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The moduli space of a smooth manifold X is defined to be the classifying space of its diffeomorphism group. Understanding the cohomology group of this space is important because elements in this group...
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural proj...
THE MODULI SPACE OF WEIGHTED CONFIGURA TIONS ON PROJECTIVE SPACE.
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
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 construct a natural smooth compacti cation of the space of smooth genus-one curves with k distinct points in a projective space. It can be viewed as an analogue of a well-known smooth compacti ca...
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...
A central question in invariant theory is that of determining the relations among invariants. Geometric invariant theory quotients come with a natural ample line bundle, and hence often a natural pr...
I give a bound on which singularities may appear on KSBA stable surfaces for a wide range of topological invariants, and use this result to describe all stable numerical quintic surfaces, i.e. stable ...
For a fixed integer l>1, we describe the singular locus of the compactification of the moduli space R_{g,l} of curves of genus g paired with an l-torsion point in their Jacobian. Generalizing previous...
Let X and X' be compact Riemann surfaces of genus at least three. Let G and G' be nontrivial connected semisimple linear algebraic groups over C. If some components $M_{DH}^d(X,G)$ and $M_{DH}^{d'}(X'...
Abstract: By using the Atiyah-Singer theorem through some similarities with the instanton and the anti-instanton moduli spaces, the dimension of the moduli space for two and four-dimensional BF theori...
We consider the moduli space of stable vector bundles on curves embedded in P2 with Hilbert polynomial 3m+ 1 and construct a compactification of this space by vector bundles. The result fM is a blow u...

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