McKay Correspondence Resolutions of Terminal Quotient Singularities G-Hilbert Scheme
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 293p-302p
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.