An explicit construction of the McKay correspondence for A-Hilb C^3

Details An explicit construction of the McKay correspondence for A-Hilb C^3 An explicit construction of the McKay correspondence for A-Hilb C^3

2000-10-05

arxiv.org/abs/math/0010053v2

Journal of Algebra 285 (2005) 682-705

Mathematics

Algebraic Geometry

25 pages, 20 figures

Scientific paper

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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