Abstract
Let α be an automorphism of the local universal deformation of a Calabi-Yau 3-manifold X, which does not act by ±id on \({H^3(X,\mathbb{C})}\). We show that the bundle \({F^2(\mathcal{H}^3)}\) in the VHS 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 α exists. Moreover we classify the possible actions of α on \({H^3(X,\mathbb{C})}\), construct examples and show that the period domain is a complex ball containing a dense set of CM points given by a Shimura datum in this case.
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Rohde, J.C. Maximal automorphisms of Calabi-Yau manifolds versus maximally unipotent monodromy. manuscripta math. 131, 459–474 (2010). https://doi.org/10.1007/s00229-009-0329-5
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DOI: https://doi.org/10.1007/s00229-009-0329-5