Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient
Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient
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DOI：
10.1215/s0012-7094-04-12422-4
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发表时间：
2002-11
影响因子：
2.5
通讯作者：
Alastair Craw;A. Ishii
中科院分区：
文献类型：
--
作者：
Alastair Craw;A. Ishii
对于SL（3，C）中的有限子群G，Bridgeland，King和Reid证明了G-簇的模空间是商C^3/G的一个可分解.本文考虑由Kronheimer引入并由Sardo Infirri进一步研究的模空间M_\theta，它与G-Hilb在GIT参数\theta的特定选择下一致.对于G的Abel算子，证明了C^3/G的每一个投射收缩分解对某个参数θ同构于M_θ.关键的一步是通过适当的傅立叶-向井变换的模空间的K-理论的GIT室的描述。我们还揭示了明确的等效性之间的衍生类别的模量M_\θ的参数躺在相邻的GIT室。
For a finite subgroup G in SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C^3/G. This paper considers the moduli spaces M_\theta, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G-Hilb for a particular choice of the GIT parameter \theta. For G Abelian, we prove that every projective crepant resolution of C^3/G is isomorphic to M_\theta for some parameter \theta. 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 M_\theta for parameters lying in adjacent GIT chambers.