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Abstract: In this paper we show that for any affine complete rational surfacesingularity there is a correspondence between the dual graph of the minimalresolution and the quiver of the endomorphism ring of the special CM modules.We thus call such an algebra the reconstruction algebra. As a consequence thederived category of the minimal resolution is equivalent to the derivedcategory of an algebra whose quiver is determined by the dual graph. Also, forany finite subgroup G of GL2,C, it means that the endomorphism ring of thespecial CM Cx,y^G modules can be used to build the dual graph of theminimal resolution of C^2-G, extending McKay-s observation for finite subgroupsof SL2,C to all finite subgroups of GL2,C.



Author: M. Wemyss

Source: https://arxiv.org/



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