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 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}
}