Duke Mathematical Journal
- Duke Math. J.
- Volume 149, Number 3 (2009), 461-507.
Derived equivalences of K3 surfaces and orientation
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
Duke Math. J., Volume 149, Number 3 (2009), 461-507.
First available in Project Euclid: 24 August 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 18E30: Derived categories, triangulated categories
Secondary: 14J28: $K3$ surfaces and Enriques surfaces
Huybrechts, Daniel; Macrì, Emanuele; Stellari, Paolo. Derived equivalences of K3 surfaces and orientation. Duke Math. J. 149 (2009), no. 3, 461--507. doi:10.1215/00127094-2009-043. https://projecteuclid.org/euclid.dmj/1251120010