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

2017/06/14 by Wahei Hara, Hara, Wahei · 7 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative property #Equivalence (formal languages) #FOS: Mathematics #Functor #Geometry #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Rings and Algebras (math.RA) #Twist

paper · pdf · doi:10.48550/arxiv.1706.04417

published in arXiv (Cornell University) (Cornell University)

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.

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• Window categories for a simple 9-fold flop of Grassmannian type
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• Derived equivalence for the simple flop of type D₄ via tilting bundles

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