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Oberseminar SoSe 2009 Zusammenfassung des Vortrags von J. C. Rohde

Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy

Assume that the local universal deformation of a Calabi-Yau 3-manifold X has an automorphism which does not act by 1 or -1 on the third cohomology. In this case X cannot be a fiber of a maximal family with maximally unipotent monodromy. Moreover one can classify the possible actions of such an automorphism on the third cohomology, construct examples and show that the period domain is a complex ball containing a dense set of complex multiplication points in this case.