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Oberseminar SoSe 2011 Zusammenfassung des Vortrags von Malek Joumaah

Finite order automorphisms of irreducible symplectic manifolds

Nikulin obtained many results about finite order automorphisms of K3 surfaces using the Torelli theorem. For irreducible holomorphic symplectic manifolds much less is known, but Verbitsky recently proved a global Torelli theorem, which can be used to construct automorphisms. We will consider an example of an automorphism of order 3 of a fourfold of type K3[2]. We will also look at examples of how the Lefschetz fixed point formula can be used to obtain information about the fixed locus from the action on cohomology.