Equivalences of twisted K3 surfaces

Details Equivalences of twisted K3 surfaces Equivalences of twisted K3 surfaces

2004-09-02

arxiv.org/abs/math/0409030v4

Mathematics

Algebraic Geometry

Final version. 35 pages. to appear in Math. Ann

Scientific paper

We prove that two derived equivalent twisted K3 surfaces have isomorphic periods. The converse is shown for K3 surfaces with large Picard number. It is also shown that all possible twisted derived equivalences between arbitrary twisted K3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a K3 surface. The passage from twisted derived equivalences to an action on the cohomology is made possible by twisted Chern characters that will be introduced for arbitrary smooth projective varieties.

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