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Variations of Hodge structure of maximal dimension. (English) Zbl 0709.14007

A general bound on the rank of period mappings \(X\to \Gamma \setminus D\) is given, improving the bound provided by J. A. Carlson in Trans. Am. Math. Soc. 294, 45-64 (1986; Zbl 0593.14006); correction ibid. 299, 429 (1987)]and by J. A. Carlson and D. Toledo in Trans. Am. Math. Soc. (to appear). Here X is any complex manifold and \(\Gamma\setminus D\) is a Griffiths period domain. This bound is shown to be sharp for X a polydisk and, with a certain exception, for X a quasi- projective variety.
Reviewer: A.Buium

MSC:

14D07 Variation of Hodge structures (algebro-geometric aspects)
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations

Citations:

Zbl 0593.14006
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References:

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