The variations of Hodge structure of maximal dimension with associated Hodge numbers ℎ^{2,0}>2 and ℎ^{1,1}=2𝑞+1 do not arise from geometry

Abstract

The specified variations are proved to be covered by a bounded contractible domain Ω \Omega . After classifying the analytic boundary components of Ω \Omega with respect to a fixed realization, the group of the biholomorphic automorphisms Aut Ω {\text {Aut}}\Omega and the Aut Ω {\text {Aut}}\Omega -orbit structure of Ω \Omega are found explicitly. Then Ω \Omega is shown to admit no quasiprojective arithmetic quotients, whereas the lack of geometrically arising variations, covered by Ω \Omega .