Geodesic
Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)
Serdica Mathematical Journal, Tome 30 (2004) no. 2-3, pp. 293-302.

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In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic group not in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to the integral cohomology on the resolution.
Keywords: McKay Correspondence, Resolutions of Terminal Quotient Singularities, G-Hilbert Scheme 
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Kędzierski, Oskar. Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1). Serdica Mathematical Journal, Tome 30 (2004) no. 2-3, pp. 293-302. http://geodesic.mathdoc.fr/item/SMJ2_2004_30_2-3_a9/