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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Azniv Kasparian
Journal: Trans. Amer. Math. Soc. 347 (1995), 4985-5007
MSC: Primary 32G20; Secondary 14C30, 14D07, 32J25
MathSciNet review: 1290721
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1290721-6
PII: S 0002-9947(1995)1290721-6
Article copyright: © Copyright 1995 American Mathematical Society