Personal tools
You are here: Home Publications Derived equivalences of K3 surfaces and orientation

Derived equivalences of K3 surfaces and orientation

Daniel Huybrechts, Emanuele Macri, Paolo Stellari

Number 22
Authors Emanuele Macrì
Daniel Huybrechts
Year 2007

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.
The appendix contains a description of Lieblich's obstruction for the deformation of complexes in families in terms of Kodaira--Spencer and Atiyah classes which is of independent interest.

More information about this publication…

Document Actions
« January 2020 »
January
MoTuWeThFrSaSu
12345
6789101112
13141516171819
20212223242526
2728293031