Stability conditions on Kuznetsov components
Arend Bayer, Martí Lahoz, Emanuele Macrì, Paolo Stellari
Abstract
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the derived category of Fano threefolds 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.
Topics & Concepts
Stability (learning theory)Fano planeStability conditionsMathematicsComponent (thermodynamics)Pure mathematicsAlgebra over a fieldComputer sciencePhysicsStatisticsThermodynamicsMachine learningDiscrete time and continuous timeHomotopy and Cohomology in Algebraic TopologyAlgebraic structures and combinatorial modelsAlgebraic Geometry and Number Theory