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Oberseminar SoSe 2011 Zusammenfassung des Vortrags von Keiji Oguiso (Osaka, JAP)

Group of automorphisms of Wehler type on Calabi-Yau manifolds and compact hyperkaehler manifolds

Wehler pointed out, without proof, that a K3 surface defined by polynomial of multi-degree (2,2,2) in the product of three projective lines admits a biholomorphic group action of the free product of three cyclic groups of order two. I would like to first explain one proof of his result and in which aspects his example is interesting. Then I would like to give a "fake" generalization for Calabi-Yau manifolds and explain why it is fake. Finally I would like to give a right generalization for Calabi-Yau manifolds of any even dimensions and compact hyperkähler manifolds of any degree.