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Geometric invariant theory and flips
We study the dependence of geometric invariant theory quotients on the choice of a linearization. We show that, in good cases, two such quotients are related by a flip in the sense of Mori, andExpand
Stable pairs, linear systems and the Verlinde formula
We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that theExpand
Conformal field theory and the cohomology of the moduli space of stable bundles
Let Σg be a compact Riemann surface of genus g ≥ 2, and let Λ be a line bundle over Σg of degree 1. Then the moduli space of rank 2 stable bundles V over Σg such that ΛV ∼= Λ was shown by SeshadriExpand
Mirror symmetry, Langlands duality, and the Hitchin system
Among the major mathematical approaches to mirror symmetry are those of Batyrev-Borisov and Strominger-Yau-Zaslow (SYZ). The first is explicit and amenable to computation but is not clearly relatedExpand
On the geometry of Deligne-Mumford stacks
General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi-)projective”Expand
Complete collineations revisited
The space of complete collineations is a compactification of the space of matrices of fixed dimension and rank, whose boundary is a divisor with normal crossings. It was introduced in the 19thExpand
Infinite Grassmannians and Moduli Spaces of G–bundles
Introduction. These are notes for my eight lectures given at the C.I.M.E. session on “Vector bundles on curves. New directions” held at Cetraro (Italy) in June 1995. The work presented here was doneExpand
On the quantum cohomology of a symmetric product of an algebraic curve
The dth symmetric product of a curve of genus g is a smooth projective variety. This paper is concerned with the little quantum cohomology ring of this variety, that is, the ring having its 3-pointExpand
Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
The moduli space of stable vector bundles on a Riemann surface is smooth when the rank and degree are coprime, and is diffeomorphic to the space of unitary connections of central constant curvature.Expand
Variation of moduli of parabolic Higgs bundles
We study moduli spaces of parabolic Higgs bundles on a curve and their dependence on the choice of weights. We describe the chamber structure on the space of weights and show that, when a wall isExpand
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