The McKay correspondence for finite subgroups of SL(3,\C)
The McKay correspondence for finite subgroups of SL(3,\C)
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DOI：
10.1515/9783110814736.221
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发表时间：
1994-11
期刊：
影响因子：
--
通讯作者：
Yukari Ito;M. Reid
中科院分区：
文献类型：
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作者：
Yukari Ito;M. Reid
这是最后的草稿，包含非常小的校对更正。设SL（n，\C）中的G是有限子群，且\fie：Y -> X = \C^n/G是商空间的奇点的任意分解.本文证明了Y的crepant例外素因子与G的“junior”共轭类一一对应。当n = 2时，这是McKay对应的一个版本（用共轭类代替G的不可约表示）。在n = 3的情形下，Roan等人的工作证明了K_Y = 0的分解存在，我们用代数圈与G的共轭类一一对应的方法证明了H^*（Y，\Q）的基的存在性.我们的治疗留下了很多问题。
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.