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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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