Derived equivalences of K3 surfaces and orientation

By D. Huybrechts, Emanuele Macrì, P. Stellari. 2007

81 citations recorded by the source corpus.

Every Fourier-Mukai equivalence between the derived categories of two K3 surfaces induces a Hodge isometry of their cohomologies viewed as Hodge structures of weight two endowed with the Mukai pairing. We prove that this Hodge isometry preserves the natural orientation of the four positive directions. This leads to a complete description of the action of the group of all autoequivalences on cohomology very much like the classical Torelli theorem for K3 surfaces determining all Hodge isometries that are induced by automorphisms.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/947a601b65c04703f3ab5f7bd61f0acb90524f05

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Stability conditions for generic K3 categories (2006, methodology): “We recall the definition of a stability condition and study the space of all stability conditions on a K3 category without (or just a few) spherical objects.”
Lectures on K3 Surfaces (2016, result): “Combining the above results with a deformation theoretic argument developed in [266] one eventually obtains”
Some moduli spaces of Bridgeland's stability conditions (2011, background): “Since Φ preserves the orientation of the Mukai lattice ([6] or Proposition 3.”
Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes (2008, background): “mation. The theory is not in its ﬁnal form, however. The obstruction class is expected to be a product of Atiyah and Kodaira–Spencer classes, but this has only been proved in some situations (such as [5]). As a consequence the results are not strong enough to obtain virtual cycles [2, 12], as discus”
Hodge theory and derived categories of cubic fourfolds (2012, unknown): “We are guided by the deformation theory for Fourier-Mukai equivalences in the wonderful papers [41, 23] 5 but with a number of simplifications and one generalisation (to Fourier-Mukai functors which are only fully faithful).”