|
This article is cited in 1 scientific paper (total in 1 paper)
On the Abuaf–Ueda Flop via Non-Commutative Crepant Resolutions
Wahei Hara The Mathematics and Statistics Building, University of Glasgow, University Place, Glasgow, G12 8QQ, UK
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.
Keywords:
derived category, non-commutative crepant resolution, flop, tilting bundle.
Received: September 30, 2020; in final form April 18, 2021; Published online April 30, 2021
Citation:
Wahei Hara, “On the Abuaf–Ueda Flop via Non-Commutative Crepant Resolutions”, SIGMA, 17 (2021), 044, 22 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1727 https://www.mathnet.ru/eng/sigma/v17/p44
|
Statistics & downloads: |
Abstract page: | 77 | Full-text PDF : | 21 | References: | 12 |
|