Hodge theory and derived categories of cubic fourfolds

Addington, Nicolas; Thomas, Robert Paul

doi:10.1215/00127094-2738639

Cited by 119 publications

(400 citation statements)

References 46 publications

(79 reference statements)

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“…Shortly after the first version of this article appeared, Addington and Thomas [AT12] announced a groundbreaking result linking the Hodge-theoretic suspicion supported by Hassett's work and the derived categorical conjecture of Kuznetsov, at least for general cubic fourfolds.…”

Section: Introductionmentioning

confidence: 99%

Cubic fourfolds containing a plane and a quintic del Pezzo surface

et al. 2014

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We isolate a class of smooth rational cubic fourfolds X containing a plane whose associated quadric surface bundle does not have a rational section. This is equivalent to the nontriviality of the Brauer class β of the even Clifford algebra over the K3 surface S of degree 2 arising from X. Specifically, we show that in the moduli space of cubic fourfolds, the intersection of divisors C 8 ∩ C 14 has five irreducible components. In the component corresponding to the existence of a tangent conic, we prove that the general member is both pfaffian and has β nontrivial. Such cubic fourfolds provide twisted derived equivalences between K3 surfaces of degrees 2 and 14, hence further corroboration of Kuznetsov's derived categorical conjecture on the rationality of cubic fourfolds.

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Section: Introductionmentioning

confidence: 99%

Cubic fourfolds containing a plane and a quintic del Pezzo surface

et al. 2014

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“…Their Hodge numbers are (h 11 , h 12 ) = (2, 32). 1 These exhaust all minimal models of X , which is the main result of this paper.…”

Section: B Howard J Nuermentioning

confidence: 80%

On (2, 4) complete intersection threefolds that contain an Enriques surface

Borisov

Nuer

2016

Math. Z.

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We study nodal complete intersection threefolds of type (2, 4) in P 5 which contain an Enriques surface in its Fano embedding. We completely determine Calabi-Yau birational models of a generic such threefold. These models have Hodge numbers h 11 = 2, h 12 = 32. We also describe Calabi-Yau varieties with Hodge numbers (h 11 , h 12 ) equal to (2, 26), (23, 5) and (31, 1). The last two pairs of Hodge numbers are, to the best of our knowledge, new.

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“…A derived categorical approach due to Kuznetsov [22] has seen recent activity [1,2,5,24]. Using the theory of semiorthogonal decompositions Kuznetsov constructs a triangulated category A X ⊂ D b (X) and conjectures that it encodes all the information concerning the rationality of X.…”

Section: Theorem 12 Let S ⊂ P 3 Be the Sextic Fermat Surface Then mentioning

confidence: 99%

“…Hence 1,1,3) , P (1,1,3,1) , P (1,3,1,1) , P (3,1,1,1) , P (5,5,5,3) , P (5,5,3,5) , P (5,3,5,5) , P (3,5,5,5) , Z (1,1,2,2) := P (1,1,2,2) , P (2,2,1,1) , P (5,5,4,4) , P (4,4,5,5) , Z (1,2,1,2) := P (1,2,1,2) , P (2,1,2,1) , P (5,4,5,4) , P (4,5,4,5) , Z (1,2,2,1) := P (1,2,2,1) , P (2,1,1,2) , P (5,4,4,5) , P (4,5,5,4) and…”

Section: The Fermat Sexticunclassified