Stability conditions on Kuznetsov components

By Arend Bayer, Mart'i Lahoz, Emanuele Macrì, P. Stellari. Annales Scientifiques de l'Ecole Normale Supérieure, 2017

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We introduce a general method to induce Bridgeland stability conditions on semiorthogonal decompositions. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the derived category of many Fano threefolds (including all but one deformation type of Picard rank one), and of cubic fourfolds. As an application, in the appendix, written jointly with Xiaolei Zhao, we give a variant of the proof of the Torelli theorem for cubic fourfolds by Huybrechts and Rennemo.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8827380993806b209f7a7d538dc882ef669e7a16