McKay correspondence and Hilbert schemes in dimension three
نویسندگان
چکیده
منابع مشابه
Mckay Correspondence and Hilbert Schemes in Dimension Three
Let G be a nontrivial finite subgroup of SLn(C). Suppose that the quotient singularity C/G has a crepant resolution π : X → C/G (i.e. KX = OX). There is a slightly imprecise conjecture, called the McKay correspondence, stating that there is a relation between the Grothendieck group (or (co)homology group) of X and the representations (or conjugacy classes) of G with a “certain compatibility” be...
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1 Introduction Conjecture 1.1 (since 1992) G ⊂ SL(n, C) is a finite subgroup. Assume that the quotient X = C n /G has a crepant resolution f : Y → X (this just means that K Y = 0, so that Y is a " noncompact Calabi–Yau manifold "). Then there exist " natural " bijections {irreducible representations of G} → basis of H * (Y, Z) (1) {conjugacy classes of G} → basis of H * (Y, Z) (2) As a slogan "...
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Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1, Gr, S2, W], but direct connections are yet to be clarified to explain such a coincidence. We provide several non-trivial steps toward establishing our main conjecture on the isomorphism between the Hilbert...
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ژورنال
عنوان ژورنال: Topology
سال: 2000
ISSN: 0040-9383
DOI: 10.1016/s0040-9383(99)00003-8