Derived equivalence for the simple flop of type D₅

2024/10/27 by Marco Rampazzo, Ying Xie, Rampazzo, Marco +1 · 2 citations
Mathematics · #14E05 #14F08 #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2410.20446

openalex publication_date 2024/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove that every simple flop of type D₅, i.e., resolved by blowups with exceptional divisor isomorphic to a generalized Grassmann bundle with fiber OG(4, 10), induces a derived equivalence. This provides new evidence for the DK conjecture of Bondal--Orlov and Kawamata. The proof is based on a sequence of mutations of exceptional objects: we use the same argument to prove derived equivalence for some pairs of non-birational Calabi--Yau fivefolds in OG(5, 10), related to Manivel's double--spinor Calabi--Yau varieties. We extend the construction to prove the derived equivalence of Calabi--Yau fibrations, which are described as zero loci in some generalized Grassmann bundles.

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• L-equivalences via Symplectic and F₄ Grassmannians
• Derived equivalence for the simple flop of type D₄ via tilting bundles

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