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Autoequivalences of twisted K3 surfaces

  • Emanuel Reinecke (a1)

Abstract

Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a given Hodge isometry arises in this way. In particular, we describe the image of the representation which associates to any autoequivalence of a twisted K3 surface its realization in cohomology: this image is a subgroup of index  $1$ or  $2$ in the group of all Hodge isometries of the twisted K3 surface. We show that both indices can occur.

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This material is based upon work supported by the National Science Foundation under grant no. DMS-1501461 and by the Studienstiftung des deutschen Volkes.

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Autoequivalences of twisted K3 surfaces

  • Emanuel Reinecke (a1)

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