Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy

Abstract

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.

main argument has been replaced by more general argument, one additional example, minor corrections, 13 pages

References in corpus (3)

• Construction and examples of higher-dimensional modular Calabi-Yau manifolds
• A very simple, robust and fast method for estimating and displaying average time constants of T2 decays from multiecho MRI images using color intensity projections
• Examples of Calabi-Yau 3-manifolds with complex multiplication

Cited by in corpus (3)

• The Picard-Fuchs equation of a family of Calabi-Yau threefolds without maximal unipotent monodromy
• Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling
• Calabi-Yau manifolds and generic Hodge groups