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Fundamental solutions of the complex Monge-Ampère equation

Halil Ibrahim Celik, Evgeny A. Poletsky (1997)

Annales Polonici Mathematici

We prove that any positive function on ℂℙ¹ which is constant outside a countable G δ -set is the order function of a fundamental solution of the complex Monge-Ampère equation on the unit ball in ℂ² with a singularity at the origin.

Gauge theoretical methods in the classification of non-Kählerian surfaces

Andrei Teleman (2009)

Banach Center Publications

The classification of class VII surfaces is a very difficult classical problem in complex geometry. It is considered by experts to be the most important gap in the Enriques-Kodaira classification table for complex surfaces. The standard conjecture concerning this problem states that any minimal class VII surface with b₂ > 0 has b₂ curves. By the results of [Ka1]-[Ka3], [Na1]-[Na3], [DOT], [OT] this conjecture (if true) would solve the classification problem completely. We explain a new approach...

Gauss-Manin connections of Schläfli type for hypersphere arrangements

Kazuhiko Aomoto (2003)

Annales de l’institut Fourier

The cohomological structure of hypersphere arragnements is given. The Gauss-Manin connections for related hypergeometrtic integrals are given in terms of invariant forms. They are used to get the explicit differential formula for the volume of a simplex whose faces are hyperspheres.

Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

Antoine Douai, Claude Sabbah (2003)

Annales de l’institut Fourier

We associate to any convenient nondegenerate Laurent polynomial f on the complex torus ( * ) n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its universal unfolding) and of the corresponding Hodge theory.

Currently displaying 1841 – 1860 of 5581