The McKay correspondence for finite subgroups of SL(3,\C)
Abstract
Description
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 exist by work of Roan and others; we prove the existence of a basis of H^*(Y, \Q) by algebraic cycles in one-to-one correspondence with conjugacy classes of G. Our treatment leaves lots of open problems.
AMSTeX, amsppt and optional epsf.tex , This paper will appear in Higher Dimensional Complex Varieties (Trento, Jun 1994), ed. M. Andreatta, De Gruyter, Mar 1996. It has been circulated as a Univ. of Tokyo, Dept. of Math Sciences preprint, UTMS 94--66, 19 pp
AMSTeX, amsppt and optional epsf.tex , This paper will appear in Higher Dimensional Complex Varieties (Trento, Jun 1994), ed. M. Andreatta, De Gruyter, Mar 1996. It has been circulated as a Univ. of Tokyo, Dept. of Math Sciences preprint, UTMS 94--66, 19 pp