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Derived equivalences of K3 surfaces and orientation

Authors
  • Huybrechts, Daniel
  • Macri, Emanuele
  • Stellari, Paolo
Type
Preprint
Publication Date
Mar 25, 2009
Submission Date
Oct 08, 2007
Source
arXiv
License
Yellow
External links

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.

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