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

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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 languageEnglish
Pages (from-to)682-705
JournalJournal of Algebra
Volume285
Issue number2
DOIs
Publication statusPublished - 15 Mar 2005

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