Derived categories of cubic fourfolds

Abstract

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.

18 pages

References in corpus (1)

• Homological projective duality for Grassmannians of lines

Cited by in corpus (59)

• Hodge theory and derived categories of cubic fourfolds
• New derived symmetries of some hyperkähler varieties
• Calabi-Yau and fractional Calabi-Yau categories
• The K3 category of a cubic fourfold
• Stability conditions on Kuznetsov components
• Derived categories view on rationality problems
• Transcendental obstructions to weak approximation on general K3 surfaces
• Stability conditions in families
• On the derived category of the classical Godeaux surface
• The Fano variety of lines and rationality problem for a cubic hypersurface
• Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
• Derived categories of Gushel-Mukai varieties
• Measures of irrationality for hypersurfaces of large degree
• Noncommutative motives of Azumaya algebras
• Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
• Gushel-Mukai varieties: linear spaces and periods
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II
• Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics
• Geometry of horospherical varieties of Picard rank one
• Küchle fivefolds of type c5
• Derived categories of cyclic covers and their branch divisors
• Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
• On the Jordan-Hölder property for geometric derived categories
• Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties
• Hodge level for weighted complete intersections
• On Küchle manifolds with Picard number greater than 1
• Cycles, derived categories, and rationality
• On the motive of O'Grady's ten-dimensional hyper-Kähler varieties
• Categorical Torelli theorems for Gushel-Mukai threefolds
• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
• On $(2,4)$ complete intersection threefolds that contain an Enriques surface
• Two-dimensional gauge dynamics and the topology of singular determinantal varieties
• Derived Equivalent Calabi-Yau 3-folds from Cubic 4-folds
• New examples of rational Gushel-Mukai fourfolds
• Symbols and equivariant birational geometry in small dimensions
• ACM bundles on cubic fourfolds containing a plane
• Purity and 2-Calabi-Yau categories
• ACM bundles on cubic threefolds
• On the derived category of ${\bar{M}}_{0,n}$
• Automorphism groups of cubic fourfolds and K3 categories
• Fano varieties of cubic fourfolds containing a plane
• On derived categories of arithmetic toric varieties
• Symmetric locally free resolutions and rationality problems
• A refined Derived Torelli Theorem for Enriques surfaces
• Equivalence of K3 surfaces from Verra threefolds
• Cubic fourfolds, Kuznetsov components and Chow motives
• Residual categories of quadric surface bundles
• Serre functors and dimensions of residual categories
• Hodge numbers and Hodge structures for Calabi-Yau categories of dimension three
• Derived categories of nodal del Pezzo threefolds
• Motives of moduli spaces on K3 surfaces and of special cubic fourfolds
• Frobenius and spherical codomains and neighbourhoods
• A family of special cubic fourfolds with motive of abelian type
• Special cubic birational transformations of projective spaces
• Semiorthogonal decomposition of ${\mathrm{D}}^b({\mathrm{Bun}}_2^L)$
• Some Moduli of $n$-pointed Fano Fourfolds
• Derived categories of quartic double fivefolds
• Consequences of the existence of exceptional collections in arithmetic and rationality
• The Intermediate Jacobian fibration of a cubic fourfold containing a plane and fibrations in Prym varieties