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 | References | Similar Articles | Additional Information

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