Derived equivalences of K3 surfaces and orientation
Abstract
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.
Keywords
Cite
@article{arxiv.0710.1645,
title = {Derived equivalences of K3 surfaces and orientation},
author = {Daniel Huybrechts and Emanuele Macri and Paolo Stellari},
journal= {arXiv preprint arXiv:0710.1645},
year = {2019}
}
Comments
This version only contains the proof that every equivalence between the derived categories of two K3 surfaces induces an orientation preserving Hodge isometry. The more formal aspects of our proof contained in the first sections of arXiv:0710.1645v2 appear now in the independent paper arXiv:0809.3201. 29 pages. Final version to appear in Duke Math. J