The McKay correspondence for finite subgroups of SL(3,\C)

```@article{Ito1994TheMC,
title={The McKay correspondence for finite subgroups of SL(3,\C)},
author={Yukari Ito and M. Reid},
journal={arXiv: Algebraic Geometry},
year={1994}
}```
• Published 1994
• Mathematics
• arXiv: Algebraic Geometry
This is the final draft, containing very minor proof-reading corrections. Let G in SL(n,\C) be a finite subgroup and \fie: Y -> X = \C^n/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime divisors of Y correspond one-to-one with ``junior'' conjugacy classes of G. When n = 2 this is a version of the McKay correspondence (with irreducible representations of G replaced by conjugacy classes). In the case n = 3, a resolution with K_Y = 0 is known to… Expand
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References

SHOWING 1-6 OF 6 REFERENCES
Gorenstein quotient singularities of monomial type in dimension three
In this paper we give an explicit description of the con- struction of 3-dimensional smooth varieties coming from a crepant reso- lution of the underlying spaces of quotient singularities C 3 /G,Expand
THE GEOMETRY OF TORIC VARIETIES
ContentsIntroductionChapter I. Affine toric varieties § 1. Cones, lattices, and semigroups § 2. The definition of an affine toric variety § 3. Properties of toric varieties § 4. Differential forms onExpand
Strings on orbifolds
• Physics
• 1985
String propagation on the quotient of a flat torus by a discrete group is considered. We obtain an exactly soluble and more or less realistic method of string compactification.