An explicit construction of the McKay correspondence for A-Hilb C3

Craw, A. (2005) An explicit construction of the McKay correspondence for A-Hilb C3. Journal of Algebra, 285(2), pp. 682-705. (doi:10.1016/j.jalgebra.2004.10.001)

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Publisher's URL: http://dx.doi.org/10.1016/j.jalgebra.2004.10.001

Abstract

For a finite Abelian subgroup A ⊂ SL(3,C), let Y=A-Hilb (C3) denote the scheme parametrising A-clusters in C3. Ito and Nakajima proved that the tautological line bundles (indexed by the irreducible representations of A) form a basis of the K-theory of Y. We establish the relations between these bundles in the Picard group of Y and hence, following a recipe introduced by Reid, construct an explicit basis of the integral cohomology of Y in one-to-one correspondence with the irreducible representations of A.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Craw, Dr Alastair
Authors: Craw, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
ISSN:0021-8693
ISSN (Online):1090-266X
Published Online:29 January 2005

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