# 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}
}
• 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…
1 Citations

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