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Equivariant Sheaves and Functors
Joseph Bernstein,Valery A. Lunts +1 more
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In this paper, the DG-modules and equivariant cohomology of toric varieties have been studied, and the derived category D G (X) and functors have been defined.Abstract:
Derived category D G (X) and functors.- DG-modules and equivariant cohomology.- Equivariant cohomology of toric varieties.read more
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From moment graphs to intersection cohomology
Tom Braden,Robert D. MacPherson +1 more
TL;DR: In this article, a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero and one-dimensional orbits.
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Knot invariants and higher representation theory I: diagrammatic and geometric categorification of tensor products
TL;DR: In this article, the authors studied 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations.
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Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
TL;DR: In this paper, it was shown that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant resolution of X=M/G and that there is a derived equivalence (Fourier- Mukai transform) between coherent sheaves on Y and coherent G-sheaves on M.
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Bimodules in bordered Heegaard Floer homology
TL;DR: In this article, the authors established naturality properties of the 3-manifold invariant and proved a duality theorem relating the two versions of the invariant to the Hochschild homology of the open book decomposition.
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More about vanishing cycles and mutation
TL;DR: In this paper, the authors continue the discussion of symplectic aspects of Picard-Lefschetz theory begun in "Vanishing cycles and mutation" and explain how to associate to a suitable fibration over a two-dimensional disc a triangulated category, the derived directed Fukaya category, which describes the structure of the vanishing cycles.