N ov 2 00 2 Flops of G - Hilb and equivalences of derived categories by variation of GIT quotient
نویسنده
چکیده
For a finite subgroup G ⊂ SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C3/G. This paper considers the moduli spaces Mθ, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G -Hilb for a particular choice of GIT parameter θ. For G Abelian, we prove that every projective crepant resolution of C3/G is isomorphic to Mθ for some parameter θ. The key step is the description of GIT chambers in terms of the K-theory of the moduli space via the appropriate Fourier-Mukai transform. We also uncover explicit equivalences between the derived categories of moduli Mθ for parameters lying in adjacent GIT chambers.
منابع مشابه
. A G ] 1 7 Fe b 20 03 Flops of G - Hilb and equivalences of derived categories by variation of GIT quotient Alastair Craw and Akira Ishii
For a finite subgroup G ⊂ SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C/G. This paper considers the moduli spaces Mθ, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G -Hilb for a particular choice of GIT parameter θ. For G Abelian, we prove that every projective crepant resolution of C/...
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