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

TL;DR

This paper proves that certain generalized Grassmannian flops of types D4 and G2 induce derived equivalences, supporting the DK conjecture through mutation techniques involving exceptional objects.

Contribution

It establishes derived equivalences for D4 and G2^{ extdagger} Grassmannian flops, providing new evidence for the DK conjecture using Kuznetsov's mutation method.

Findings

Derived equivalences for D4 and G2^{ extdagger} flops

Supports DK conjecture with new cases

Uses mutation of exceptional objects

Abstract

We prove that the generalized Grassmannian flops of both $D_4$ and $G_2^{\dagger}$ 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.