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Geometric invariant theory and flips

- M. Thaddeus
- Mathematics
- 10 May 1994

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, and… Expand

Stable pairs, linear systems and the Verlinde formula

- M. Thaddeus
- Mathematics
- 19 October 1992

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 the… Expand

Conformal field theory and the cohomology of the moduli space of stable bundles

- M. Thaddeus
- Mathematics
- 1992

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 Seshadri… Expand

Mirror symmetry, Langlands duality, and the Hitchin system

- Tamás Hausel, M. Thaddeus
- Mathematics, Physics
- 23 May 2002

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 related… Expand

On the geometry of Deligne-Mumford stacks

- A. Kresch, D. Abramovich, A. Bertram, L. Katzarkov, R. Pandharipande, M. Thaddeus
- Mathematics
- 2009

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

- M. Thaddeus
- Mathematics
- 27 August 1998

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 19th… Expand

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 done… Expand

On the quantum cohomology of a symmetric product of an algebraic curve

- A. Bertram, M. Thaddeus
- Mathematics
- 9 March 1998

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-point… Expand

Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles

- Tamás Hausel, M. Thaddeus
- Mathematics, Physics
- 16 March 2000

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

- M. Thaddeus
- Mathematics
- 30 March 2000

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 is… Expand

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