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Bounds of the dimension of variations of Hodge structure. (English) Zbl 0593.14006

An image of the ”period mapping” from the base space of a smooth family of projective varieties into the classifying space D for Hodge structures is called a geometrical variation (g. v.) and is an integral variety of distribution on D defined by Griffiths’ condition \(dF^ p/dt\subset F^{p-1}\) for a one-parameter g. v. of Hodge filtration \(...\subset F^ p\subset F^{p-1}\subset...\) For Hodge structures of weight 2 (when \(h^{2,0}\), \(h^{1,1}\) only exist) with \(h^{2,0}>1\) as upper bound for the dimension of integral varieties is found \(h^{2,0}h^{1,1}\) and examples of g. v. for which this bound is arrived are given. Some higher weight generalizations are considered.
Reviewer: A.Givental’

MSC:

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