Abstract
We introduce a new class of algebras, called reconstruction algebras, and present some of their basic properties. These non-commutative rings dictate in every way the process of resolving the Cohen-Macaulay singularities C 2 / G \mathbb {C}^2/G where G = 1 r ( 1 , a ) ≤ G L ( 2 , C ) G=\frac {1}{r}(1,a)\leq GL(2,\mathbb {C}) .
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