# On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions

@article{Hara2018OnTA, title={On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions}, author={Wahei Hara}, journal={arXiv: Algebraic Geometry}, year={2018} }

The Abuaf-Ueda flop is a $7$-dimensional flop related to $G_2$ homogeneous spaces. The derived equivalence for this flop is first proved by Ueda using mutations of semi-orthogonal decompositions. In this article, we give an alternative proof for the derived equivalence in which we use tilting bundles. Our proof also show the existence of non-commutative crepant resolutions of the singularity appearing in the flopping contraction. We also give some results on moduli spaces of finite-length…

## One Citation

### Non-commutative crepant resolutions, an overview

- Mathematics
- 2022

Non-commutative crepant resolutions (NCCRs) are non-commutative analogues of the usual crepant resolutions that appear in algebraic geometry. In this paper we survey some results around NCCRs.

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