Twisted Fourier–Mukai functors

Canonaco, Alberto; Stellari, Paolo

doi:10.1016/j.aim.2006.10.010

Cited by 51 publications

(80 citation statements)

References 8 publications

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“…7.10], given any K3 surface S and any nontrivial β ∈ Br(S), there is no equivalence between D b (S, β) and D b (S). Thus any X as in Corollary B validates Kuznetsov's conjecture, but not via the K3 surface S. Moreover, S and S are twisted Fourier-Mukai partners: by [CS07,Thm. 5.1], the equivalence…”

Section: The Twisted Derived Equivalencementioning

confidence: 48%

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: The Twisted Derived Equivalencementioning

confidence: 48%

Cubic fourfolds containing a plane and a quintic del Pezzo surface

et al. 2014

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“…where p i : X 1 ×X 2 → X i is the projection and i ∈ {1, 2} (see also [6] for a more general statement). The complex E is the kernel of and it is uniquely (up to isomorphism) determined.…”

Section: Derived Categories Of Abelian Varieties and K3 Surfacesmentioning

confidence: 99%

Derived categories and Kummer varieties

Stellari

2007

Math. Z.

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“…By the theorem of Canonaco-Stellari ( [3]), every equivalence between derived categories of twisted K3 surfaces is of Fourier-Mukai type. Thus only "if" part requires an explanation.…”

Section: S) If and Only If There Exists A Hodge Isometry T (S)mentioning

confidence: 99%

“…3 Lattice-theoretic descriptions 3.1 Isotropic elements of the discriminant form Let (S, α) be a twisted K3 surface. We write T := T (S, α), which is an even lattice of sign(T ) = (2, 20 − ρ(S)) equipped with a period.…”

Section: S) If and Only If There Exists A Hodge Isometry T (S)mentioning

confidence: 99%

Twisted Fourier-Mukai number of a $K3$ surface

2009

Trans. Amer. Math. Soc.

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Twisted Fourier–Mukai functors

Cited by 51 publications

References 8 publications

Cubic fourfolds containing a plane and a quintic del Pezzo surface

Cubic fourfolds containing a plane and a quintic del Pezzo surface

Derived categories and Kummer varieties

Twisted Fourier-Mukai number of a $K3$ surface

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