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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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: http://dx.doi.org/10.1090/S0002-9947-99-02395-8
PII: S 0002-9947(99)02395-8
Received by editor(s): December 5, 1997
Published electronically: July 26, 1999
Article copyright: © Copyright 2000 American Mathematical Society