Kavli Affiliate: Yukari Ito
| Summary:
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.
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