Crepant resolutions of orbifolds by variation of GIT quotients
-- Alastair Craw, September 12, 2003

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For a finite subgroup G of SL(3,C), Bridgeland, King and Reid proved that
a particular crepant resolution of the quotient C^3/G is "distinguished"
in the sense that it is a moduli space of objects on C^3.  This result
appears to contradict standard threefold ideology requiring that any one
minimal model should be as good as any other. I'll describe recent joint
work with A. Ishii (Kyoto) proving that every crepant resolution of C^3/G
is a moduli space of representations of the McKay quiver (for G Abelian),
generalising the result by Kronheimer for finite subgroups of SL(2,C).