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Variations of Hodge structure, Legendre submanifolds, and accessibility


Authors: James A. Carlson and Domingo Toledo
Journal: Trans. Amer. Math. Soc. 311 (1989), 391-411
MSC: Primary 32G20
DOI: https://doi.org/10.1090/S0002-9947-1989-0974782-4
MathSciNet review: 974782
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Abstract: Variations of Hodge structure of weight two are integral manifolds for a distribution in the tangent bundle of a period domain. This distribution has dimension $ {h^{2,0}}{h^{1,1}}$ and is nonintegrable for $ {h^{2,0}} > 1$. In this case it is known that the dimension of an integral manifold does not exceed $ \frac{1} {2}{h^{2,0}}{h^{1,1}}$. Here we give a new proof, based on an analogy between Griffiths' horizontal differential system of algebraic geometry and the contact system of classical mechanics. We show also that any two points in such a domain can be joined by a horizontal curve which is piecewise holomorphic.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0974782-4
Article copyright: © Copyright 1989 American Mathematical Society

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