On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists

2017/06/14 by Wahei Hara, Hara, Wahei · 4 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1706.04417

openalex publication_date 2017/06/14 · openalex created_date 2017/06/23 · openalex updated_date 2026/07/28

Abstract

Recently, Segal constructed a derived equivalence for an interesting 5-fold flop that was provided by Abuaf. The aim of this article is to add some results for the derived equivalence for Abuaf's flop. Concretely, we study the equivalence for Abuaf's flop by using Toda-Uehara's tilting bundles and Iyama-Wemyss's mutation functors. In addition, we observe a "flop-flop=twist" result and a "multi-mutation=twist" result for Abuaf's flop.

Cited by

• A simpler kernel for stratified Mukai flops
• Window categories for a simple 9-fold flop of Grassmannian type
• Spherical functors and the flop-flop autoequivalence
• Derived equivalence for the simple flop of type D₄ via tilting bundles

Related

• On some examples of spherical functors related to flops
• Spherical functors and the flop-flop autoequivalence
• Derived equivalence for the simple flop of type G₂^† via tilting bundles
• Deformation of tilting-type derived equivalences for crepant resolutions
• A categorical flop in dimension one