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Autoequivalences of twisted K3 surfaces
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 5 / May 2019
- Published online by Cambridge University Press:
- 30 April 2019, pp. 912-937
- Print publication:
- May 2019
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- Article
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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.
