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

Alastair Craw

doi:10.1016/j.jalgebra.2004.10.001

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

Alastair Craw

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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Abstract

For a finite Abelian subgroup A of SL(3,C), Ito and Nakajima proved that the tautological bundles on the A-Hilbert scheme Y = A-Hilb(C^3) 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.

Original language	English
Pages (from-to)	682-705
Journal	Journal of Algebra
Volume	285
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2004.10.001
Publication status	Published - 15 Mar 2005

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abstract = "For a finite Abelian subgroup A of SL(3,C), Ito and Nakajima proved that the tautological bundles on the A-Hilbert scheme Y = A-Hilb(C^3) 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.",

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AB - For a finite Abelian subgroup A of SL(3,C), Ito and Nakajima proved that the tautological bundles on the A-Hilbert scheme Y = A-Hilb(C^3) 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.

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