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Title:
Parabolic automorphisms of hyperkähler manifolds
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Abstract:
As observed by Serge Cantat, an automorphism of a K3 surface which is a fiberwise translation in an elliptic pencil acts with dense orbits in the fibers; as a consequence, if a K3 surface has two such automorphisms (with distinct pencils), then the group they generate acts ergodically. We show that the same holds for arbitrary hyperkähler manifolds, as an application of Deligne semisimplicity theorem. This is a joint work with Misha Verbitsky.
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