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

  title={On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions},
  author={Wahei Hara},
  journal={arXiv: Algebraic Geometry},
  • Wahei Hara
  • Published 27 December 2018
  • Mathematics
  • arXiv: Algebraic Geometry
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… 
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