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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Bounds on the dimension of variations of Hodge structure


Author: James A. Carlson
Journal: Trans. Amer. Math. Soc. 294 (1986), 45-64
MSC: Primary 14D05; Secondary 14C30, 32G20
DOI: https://doi.org/10.1090/S0002-9947-1986-0819934-6
Erratum: Trans. Amer. Math. Soc. 299 (1987), 429.
MathSciNet review: 819934
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Abstract: We derive upper bounds on the dimension of a variation of Hodge structure of weight two and show that these bounds are sharp. Using them we exhibit maximal geometric variations of Hodge structure. Analogous results for higher weight are obtained in the presence of a nondegeneracy hypothesis, and variations coming from hypersurfaces are shown to be nondegenerate. Maximal geometric variations of higher weight are also constructed.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0819934-6
Article copyright: © Copyright 1986 American Mathematical Society