On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists

Abstract

Recently, Segal constructed a derived equivalence for an interesting 5-fold flop that was provided by Abuaf. The aim of this article is to add some results for the derived equivalence for Abuaf's flop. Concretely, we study the equivalence for Abuaf's flop by using Toda-Uehara's tilting bundles and Iyama-Wemyss's mutation functors. In addition, we observe a "flop-flop=twist" result and a "multi-mutation=twist" result for Abuaf's flop.Comment: 38 pages, v2;major revision. improved the readability of proofs, Appendix C adde