Variations of Hodge structure, Legendre submanifolds, and accessibility
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- by James A. Carlson and Domingo Toledo PDF
- Trans. Amer. Math. Soc. 311 (1989), 391-411 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- 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