منابع مشابه
Hodge equations with change of type
A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces in the elliptic region to the equations for harmonic 1-forms on the projective disc is studied in detail. A boundary-value problem for this example is formulated and is shown to possess weak solutions. MSC2000: 35M10, 58J99.
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We show that any effective Hodge structure of CMtype occurs (without having to take a Tate twist) in the cohomology of some CM abelian variety over C. As a consequence we get a simple proof of the theorem (due to Hazama) that the usual Hodge conjecture for the class of all CM abelian varieties implies the general Hodge conjecture for the same class.
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Given a variation of Hodge structure over P with Hodge numbers (1, 1, . . . , 1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin–Kontsevich–Möller–Zorich, by using the local exponents of the corresponding Picard– Fuchs equation. This allows us to compute the Hodge numbers of Zucker’s Hodge structure on the corresponding parabolic cohomology gro...
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A gauge-invariant form of the nonlinear Hodge equations is studied. 1991 MSC: 58E15 (Classical field theory)
متن کاملHodge Groups of Hodge Structures with Hodge Numbers
This paper studies the possible Hodge groups of simple polarizable Q-Hodge structures with Hodge numbers (n, 0, . . . , 0, n). In particular, it generalizes earlier work of Ribet and MoonenZarhin to completely determine the possible Hodge groups of such Hodge structures when n is equal to 1, 4, or a prime p. In addition, the paper determines possible Hodge groups, under certain conditions on th...
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ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata
سال: 2002
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-002-0049-x