Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy

Details Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy

2009-02-26

arxiv.org/abs/0902.4592v2

Mathematics

Algebraic Geometry

main argument has been replaced by more general argument, one additional example, minor corrections, 13 pages

Scientific paper

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. We show that the $F^2$ bundle in the Variation of Hodge structures of each maximal family containing $X$ is constant in this case. Thus X cannot be a fiber of a maximal family with maximally unipotent monodromy, if such an automorphism exists. Moreover we 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.

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