Derived Equivalences of Generalized Grassmannian Flops: D₄ and G₂^† Cases

2024/12/22 by Ying Xie, Xie, Ying
Physics and Astronomy · Mathematics · Medicine · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2412.17130

Abstract

We prove that the generalized Grassmannian flops of both D₄ and G₂^† type induce derived equivalences, which provide new evidence for the DK conjecture by Bondal-Orlov and Kawamta. The proof is based on Kuznetsov's mutation technique, which takes a sequence of mutations of exceptional objects.

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