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

Kasparian, Azniv

doi:10.1090/S0002-9947-1995-1290721-6

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
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Trans. Amer. Math. Soc. 347 (1995), 4985-5007 Request permission

Abstract:

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

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