The $${{\rm GL}(2,\mathbb{C})}$$ McKay correspondence |
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Authors: | Michael Wemyss |
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Institution: | 1.Mathematical Institute,Oxford,UK |
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Abstract: | In this paper we show that for any affine complete rational surface singularity the quiver of the reconstruction algebra can
be determined combinatorially from the dual graph of the minimal resolution. As a consequence the derived category of the
minimal resolution is equivalent to the derived category of an algebra whose quiver is determined by the dual graph. Also,
for any finite subgroup G of
GL(2,\mathbbC){{\rm GL}(2,\mathbb{C})}, it means that the endomorphism ring of the special CM
\mathbbC{\mathbb{C}} x, y]]
G
-modules can be used to build the dual graph of the minimal resolution of
\mathbbC2/G{\mathbb{C}^{2}/G}, extending McKay’s observation (McKay, Proc Symp Pure Math, 37:183–186, 1980) for finite subgroups of
SL(2,\mathbbC){{\rm SL}(2,\mathbb{C})} to all finite subgroups of
GL(2,\mathbbC){{\rm GL}(2,\mathbb{C})}. |
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Keywords: | |
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