English

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

Algebraic Geometry 2021-05-03 v3 Rings and Algebras

Abstract

The Abuaf-Ueda flop is a 7-dimensional flop related to G2G_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.

Keywords

Cite

@article{arxiv.1812.10688,
  title  = {On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions},
  author = {Wahei Hara},
  journal= {arXiv preprint arXiv:1812.10688},
  year   = {2021}
}