Stability conditions on triangulated categories
- T. Bridgeland
- Mathematics
- 17 December 2002
This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's…
Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
- T. Bridgeland, A. King, M. Reid
- Mathematics
- 6 August 1999
Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M…
Stability conditions on $K3$ surfaces
- T. Bridgeland
- Mathematics
- 11 July 2003
This paper contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface.
Flops and derived categories
- T. Bridgeland
- Mathematics
- 6 September 2000
This paper contains some applications of Fourier-Mukai techniques to the birational geometry of threefolds. In particular, we prove that birational Calabi-Yau threefolds have equivalent derived…
Equivalences of Triangulated Categories and Fourier–Mukai Transforms
- T. Bridgeland
- Mathematics
- 21 September 1998
We give a condition for an exact functor between triangulated categories to be an equivalence. Applications to Fourier–Mukai transforms are discussed. In particular, we obtain a large number of such…
Derived categories of coherent sheaves
- T. Bridgeland
- Mathematics
- 7 February 2006
We discuss derived categories of coherent sheaves on algebraic varieties. We focus
on the case of non-singular Calabi�Yau varieties and consider two unsolved problems: proving
that birational…
Quantum groups via Hall algebras of complexes
- T. Bridgeland
- Mathematics
- 3 November 2011
We describe quantum enveloping algebras of symmetric Kac-Moody Lie algebras via a finite field Hall algebra construction involving Z_2-graded complexes of quiver representations.
Hall algebras and curve-counting invariants
- T. Bridgeland
- Mathematics
- 23 February 2010
We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating…
T-structures on some local Calabi–Yau varieties
- T. Bridgeland
- Mathematics
- 2 February 2005
Fourier-Mukai transforms for elliptic surfaces
- T. Bridgeland
- Mathematics
- 1 May 1997
We compute a large number of moduli spaces of stable bun- dles on a general algebraic elliptic surface using a new class of relative Fourier-Mukai transforms.
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