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

Author:
Richárd Mayer

Journal:
Trans. Amer. Math. Soc. **352** (2000), 2121-2144

MSC (1991):
Primary 14C30

DOI:
https://doi.org/10.1090/S0002-9947-99-02395-8

Published electronically:
July 26, 1999

MathSciNet review:
1624194

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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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Additional Information

**Richárd Mayer**

Affiliation:
Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003

Email:
mayer@math.umass.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02395-8

Received by editor(s):
December 5, 1997

Published electronically:
July 26, 1999

Article copyright:
© Copyright 2000
American Mathematical Society