Twisted Fourier–Mukai functors

By Alberto Canonaco, P. Stellari. 2006

87 citations recorded by the source corpus.

Due to a theorem by Orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of Fourier?Mukai type. We extend this result to the case of bounded derived categories of twisted coherent sheaves and at the same time we weaken the hypotheses on the functor. As an application we get a complete description of the exact functors between the abelian categories of twisted coherent sheaves on smooth projective varieties.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82f00028306af04997036bbb2991315356af51c2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stability conditions for generic K3 categories (2006, methodology): “In the following we shall tacitly use that any equivalence is of Fourier–Mukai type, which was proved by Orlov in [22] in the untwisted case and in [8] in general.”
A tour about existence and uniqueness of dg enhancements and lifts (2016, background): “The result has been generalized to the twisted setting under milder assumptions on the functor in [16].”
Lectures on K3 Surfaces (2016, methodology): “The Fourier–Mukai formalism can be developed in the twisted context and, as proved by Canonaco and Stellari in [98], any exact linear equivalence between twisted derived categories is of Fourier–Mukai type.”
Projectivity and birational geometry of Bridgeland moduli spaces (2012, unknown): “Since everything is compatible with Fourier–Mukai equivalences, this follows from [17,70].”
Fano varieties of cubic fourfolds containing a plane (2009, unknown): “Due to (∗), there is a an equivalence Φ : Db(S, β) ∼ −→ Db(S′) which, in view of [9], is a Fourier–Mukai functor ΦE .”