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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.
S. Tregub, Three constructions of rationality of a cubic fourfold
1984
Earlier work this paper cites.
A. Bondal, Representations of associative algebras and coherent sheaves
1990
Earlier work this paper cites.
A. Bondal, M. Kapranov, Representable functors, Serre functors, and reconstructions
1990
Earlier work this paper cites.
D. Orlov, Projective bundles, monoidal transformations, and derived categories of coherent sheaves
1993
Cited alongside, same era.
S. Tregub, Two remarks on four dimensional cubics
1993
Cited alongside, same era.
B. Hassett, Special Cubic Fourfolds
1998
Cited alongside, same era.
A. Bondal, D. Orlov, Semiorthogonal decomposition for algebraic varieties
Cited in the paper.
D. Huybrechts, P. Stellari, Equivalences of twisted K3 surfaces
Cited in the paper.
D. Huybrechts, P. Stellari, Proof of Căldăraru’s conjecture
Cited in the paper.
A. Kuznetsov, Homological projective duality for Grassmannians of lines
Cited in the paper.
A. Kuznetsov, Derived categories and rationality
Cited in the paper.
B. Hassett, Special cubic fourfolds
2000
Later among the works it cites.
A. Kuznetsov, Derived categories of quadric fibrations and intersections of quadrics
2008
Closest in time.
A. Kuznetsov, Lefschetz decompositions and categorical resolutions of singularities
2008
Closest in time.
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