Derived equivalences of K3 surfaces and orientation

Details Derived equivalences of K3 surfaces and orientation Derived equivalences of K3 surfaces and orientation

2007-10-08

arxiv.org/abs/0710.1645v4

Mathematics

Algebraic Geometry

This version only contains the proof that every equivalence between the derived categories of two K3 surfaces induces an orien

Scientific paper

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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