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arXiv · 1812.10688

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

Wahei Hara
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Abstract

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

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Wahei Hara. 2018-12-27. On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions. https://doi.org/10.3842/sigma.2021.044

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