Coupled Contact Systems and Rigidity of Maximal Dimensional Variations of Hodge Structure

Details Coupled Contact Systems and Rigidity of Maximal Dimensional Variations of Hodge Structure Coupled Contact Systems and Rigidity of Maximal Dimensional Variations of Hodge Structure

1997-11-30

arxiv.org/abs/alg-geom/9712001v1

Mathematics

Algebraic Geometry

24 pages, latex2e uses amsart.cls

Scientific paper

In this article we prove that locally Griffiths' horizontal distribution on the period domain is given by a generalized version of the familiar contact differential system. As a consequence of this description we obtain strong local rigidity properties of maximal dimensional variations of Hodge structure. For example, we prove that if the weight is odd then there is a unique germ of maximal dimensional variation of Hodge stucture though every point of the period domain. Similar results hold if the weight is even with the exception of one case.

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