Coupled contact systems and rigidity of maximal dimensional variations of Hodge structure

Mayer, Richárd

doi:10.1090/S0002-9947-99-02395-8

Coupled contact systems and rigidity of maximal dimensional variations of Hodge structure
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Trans. Amer. Math. Soc. 352 (2000), 2121-2144 Request permission

Abstract:

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 (greater than one) then there is a unique germ of maximal dimensional variation of Hodge structure through every point of the period domain. Similar results hold if the weight is even with the exception of one case.

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