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Mathematics > Algebraic Geometry

arXiv:1812.10688 (math)
[Submitted on 27 Dec 2018 (v1), last revised 30 Apr 2021 (this version, v3)]

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

Authors: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.
Subjects: Algebraic Geometry (math.AG); Rings and Algebras (math.RA)
Cite as: arXiv:1812.10688 [math.AG]
  (or arXiv:1812.10688v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.10688
Journal reference: SIGMA 17 (2021), 044, 22 pages
Related DOI: https://doi.org/10.3842/SIGMA.2021.044

Submission history

From: Wahei Hara [view email] [via SIGMA proxy]
[v1] Thu, 27 Dec 2018 10:38:35 UTC (19 KB)
[v2] Tue, 29 Sep 2020 16:12:47 UTC (18 KB)
[v3] Fri, 30 Apr 2021 05:16:07 UTC (22 KB)
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