Derived equivalence for the simple flop of type $G_2^{\dagger}$ via tilting bundles

Wahei Hara

doi:10.1016/j.jalgebra.2026.03.041

paper

Derived equivalence for the simple flop of type $G_{2}^{†}$ via tilting bundles

arXiv:2412.14314 · doi:10.1016/j.jalgebra.2026.03.041

Abstract

The aim of this article is to prove the derived equivalence for a local model of the simple flop of type $G_{2}^{†}$ , which was found by Kanemitsu. This flop is the only known simple flop that comes from a non-homogeneous roof. The proof of the derived equivalence is done by using tilting bundles, and also produces a noncommutative crepant resolution of the singularity that is derived equivalent to both sides of the flop.

11 pages, accepted version

Derived equivalence for the simple flop of type G2†​ via tilting bundles

Abstract

Derived equivalence for the simple flop of type $G_{2}^{†}$ via tilting bundles