Isomorphism Problems of Noncommutative Deformations of Type D Kleinian Singularities

Abstract

We construct all possible noncommutative deformations of a Kleinian singularity ${\mathbb{C}}^2/\Gamma$ of type $D_n$ in terms of generators and relations, and solve the problem of when two deformations are isomorphic. We prove that all isomorphisms arise naturally from the action of the normalizer $N_{\SL(2)}(Γ)$ on $\mathbb{C}/\Gamma$. We deduce that the moduli space of isomorphism classes of noncommutative deformations in type $D_n$ is isomorphic to a vector space of dimension $n$.

24 pages

Cited by in corpus (2)

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