• Corpus ID: 119274539

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}
}

• Martin Kalck, J. Karmazyn
• Published 10 July 2017
• Mathematics
• arXiv: Algebraic Geometry

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 singularity categories, and an idea of Hille & Ploog yielding strongly quasi-hereditary algebras which we describe explicitly by building on Wemyss's work on reconstruction algebras. Moreover, K-theory gives obstructions to generalisations of our main result.