Stability conditions on Kuznetsov components

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.

53 pages. Appendix about the Torelli theorem for cubic fourfolds by A. Bayer, M. Lahoz, E. Macrì, P. Stellari, and X. Zhao. Final version to appear in Ann. Sci. Éc. Norm. Supér

References in corpus (24)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Semiorthogonal decomposition for algebraic varieties
• Derived categories of cubic fourfolds
• Hodge theory and derived categories of cubic fourfolds
• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Semiorthogonal decompositions in algebraic geometry
• A global Torelli theorem for hyperkahler manifolds
• Hochschild homology and semiorthogonal decompositions
• The K3 category of a cubic fourfold
• Derived categories view on rationality problems
• Stability conditions in families
• Birational models of moduli spaces of coherent sheaves on the projective plane
• Derived categories of cubic and V14 threefolds
• Stability conditions on Fano threefolds of Picard number one
• Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
• A remark on the Torelli theorem for cubic fourfolds
• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• Stability conditions, Bogomolov-Gieseker type inequalities and Fano 3-folds
• Generalized Bogomolov-Gieseker type inequalities on Fano 3-folds
• Stability conditions on curves
• ACM bundles on cubic threefolds
• Hochschild cohomology versus the Jacobian ring, and the Torelli theorem for cubic fourfolds
• Hodge numbers of moduli spaces of stable bundles on K3 surfaces
• Derived Categories of Quadric Fibrations and Intersections of Quadrics

Cited by in corpus (24)

• Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
• The desingularization of the theta divisor of a cubic threefold as a moduli space
• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• Some remarks on Fano threefolds of index two and stability conditions
• On the Chow theory of projectivizations
• Categorical Torelli theorems for Gushel-Mukai threefolds
• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
• Moduli spaces of Ulrich bundles on the Fano 3-fold $V_5$
• On the double EPW sextic associated to a Gushel-Mukai fourfold
• The Voisin map via families of extensions
• Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$
• Stability conditions on product varieties
• Purity and 2-Calabi-Yau categories
• K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration
• Automorphism groups of cubic fourfolds and K3 categories
• Bridgeland stability of minimal instanton bundles on Fano threefolds
• Rational cubic fourfolds in Hassett divisors
• Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture
• A refined Derived Torelli Theorem for Enriques surfaces
• Serre functors and dimensions of residual categories
• On the Bogomolov-Gieseker inequality in positive characteristic
• Bridgeland stability conditions on the category of holomorphic triples over curves
• Chern degree functions
• Some quadratic inequalities on product varieties