Stability conditions on Kuznetsov components

Arend Bayer, Marti Lahoz, Emanuele Macri, Paolo Stellari

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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.
Original languageEnglish
Number of pages55
JournalAnnales Scientifiques de l'École Normale Supérieure
Publication statusAccepted/In press - 4 May 2021

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