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Equivalences of twisted K3 surfaces

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Abstract

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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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Beringstr. 1, D-53115, Bonn, Germany

    Daniel Huybrechts

  2. Department of Mathematics, Università degli Studi di Milano, Via Cesare Saldini 50, 20133, Milan, Italy

    Paolo Stellari

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  1. Daniel Huybrechts
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  2. Paolo Stellari
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Correspondence to Daniel Huybrechts.

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Huybrechts, D., Stellari, P. Equivalences of twisted K3 surfaces. Math. Ann. 332, 901–936 (2005). https://doi.org/10.1007/s00208-005-0662-2

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