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

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.

References in corpus (3)

• Derived equivalence of Ito-Miura-Okawa-Ueda Calabi-Yau 3-folds
• On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists
• Mukai pairs and simple $K$-equivalence

Cited by in corpus (1)

• Full exceptional collections for anticanonical log del Pezzo surfaces