Abstract
Abstract Let G be a finite subgroup of GL(2) acting on A2/{0} freely. The G-orbit Hilbert scheme G-Hilb(A2) is a minimal resolution of the quotient A2/G as given by A. Ishii, On the McKay correspondence for a finite small subgroup of GL(2,C), J. Reine Angew. Math. 549 (2002), 221–233. We determine the generator sheaf of the ideal defining the universal G-cluster over G-Hilb(A2), which somewhat strengthens a version [10] of the well-known McKay correspondence for a finite subgroup of SL(2).
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