منابع مشابه
Quiver Varieties and Tensor Products
In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety Z̃ in a quiver variety, and show the following results: (1) The homology group of Z̃ is a representation of a symmetric Kac-Moody Lie algebra g, isomorphic to the tensor product V (λ1)⊗· · ·⊗V (λN ) of integrable highest weight modu...
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Braverman-Finkelberg [4] recently propose the geometric Satake correspondence for the affine Kac-Moody group Gaff . They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of Gcpt-instantons on R /Zr correspond to weight spaces of representations of the Langlands dual group G∨aff at level r. When G = SL(l), the Uhlenbeck compactification...
متن کاملSmoothing of Quiver Varieties
We show that Gorenstein singularities that are cones over singular Fano varieties provided by so-called flag quivers are smoothable in codimension three. Moreover, we give a precise characterization about the smoothability in codimension three of the Fano variety itself.
متن کاملQuiver Varieties and Hilbert Schemes
In this note we give an explicit geometric description of some of the Nakajima’s quiver varieties. More precisely, if X = C, Γ ⊂ SL(C) is a finite subgroup, and XΓ is a minimal resolution of X/Γ, we show that X (the Γ-equivariant Hilbert scheme of X), and X [n] Γ (the Hilbert scheme of XΓ) are quiver varieties for the affine Dynkin graph corresponding to Γ via the McKay correspondence with the ...
متن کاملProblems on Quiver Varieties
(1) Study the class of hyper-Kähler manifolds which are hyper-Kähler reductions of finite dimensional quaternion vector spaces by products of unitary groups. (Probably it is better to assume that the action is linear.) Besides quiver varieties, hyper-Kähler toric varieties in the sense of Bielawski and Dancer [2] are such examples. When the quotients are nonsingular ? How much of geometric prop...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2001
ISSN: 0020-9910
DOI: 10.1007/pl00005810