Derived equivalence for the simple flop of type $D_5$

Marco Rampazzo; Ying Xie

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arXiv · 2410.20446

Derived equivalence for the simple flop of type $D_5$

Marco Rampazzo·Ying Xie

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Abstract

We prove that every simple flop of type $D_5$, 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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Marco Rampazzo, Ying Xie. 2024-10-27. Derived equivalence for the simple flop of type $D_5$. https://arxiv.org/abs/2410.20446

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