Derived Equivalences of Generalized Grassmannian Flops: $D_4$ and $G_2^{\dagger}$ Cases

Ying Xie

paper

Derived Equivalences of Generalized Grassmannian Flops: $D_{4}$ and $G_{2}^{†}$ Cases

arXiv:2412.17130

Abstract

We prove that the generalized Grassmannian flops of both $D_{4}$ and $G_{2}^{†}$ 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.

23 pages. Comments are welcome!

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

Abstract

Derived Equivalences of Generalized Grassmannian Flops: $D_{4}$ and $G_{2}^{†}$ Cases