# Noncommutative Kn\"orrer type equivalences via noncommutative resolutions of singularities

@article{Kalck2017NoncommutativeKT, title={Noncommutative Kn\"orrer type equivalences via noncommutative resolutions of singularities}, author={Martin Kalck and Joseph Karmazyn}, journal={arXiv: Algebraic Geometry}, year={2017} }

We construct Kn\"orrer type equivalences outside of the hypersurface case, namely, between singularity categories of cyclic quotient surface singularities and certain finite dimensional local algebras. This generalises Kn\"orrer's equivalence for singularities of Dynkin type A (between Krull dimensions $2$ and $0$) and yields many new equivalences between singularity categories of finite dimensional algebras. Our construction uses noncommutative resolutions of singularities, relative…

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