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Proof of Nadel’s conjecture and direct image for relative K -theory

Alain Berthomieu (2002)

Bulletin de la Société Mathématique de France

A “relative” K -theory group for holomorphic or algebraic vector bundles on a compact or quasiprojective complex manifold is constructed, and Chern-Simons type characteristic classes are defined on this group in the spirit of Nadel. In the projective case, their coincidence with the Abel-Jacobi image of the Chern classes of the bundles is proved. Some applications to families of holomorphic bundles are given and two Riemann-Roch type theorems are proved for these classes.

Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels

E. H. Youssfi (2002)

Studia Mathematica

We consider a large class of convex circular domains in M m ₁ , n ₁ ( ℂ ) × . . . × M m d , n d ( ℂ ) which contains the oval domains and minimal balls. We compute their Bergman and Szegő kernels. Our approach relies on the analysis of some proper holomorphic liftings of our domains to some suitable manifolds.

Proper holomorphic mappings between rigid polynomial domains in Cn+1.

Bernard Coupet, Nabil Ourimi (2001)

Publicacions Matemàtiques

We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in Cn+1. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.

Proper holomorphic mappings vs. peak points and Shilov boundary

Łukasz Kosiński, Włodzimierz Zwonek (2013)

Annales Polonici Mathematici

We present a result on the existence of some kind of peak functions for ℂ-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for A(D) under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.

Proper holomorphic self-mappings of the minimal ball

Nabil Ourimi (2002)

Annales Polonici Mathematici

The purpose of this paper is to prove that proper holomorphic self-mappings of the minimal ball are biholomorphic. The proof uses the scaling technique applied at a singular point and relies on the fact that a proper holomorphic mapping f: D → Ω with branch locus V f is factored by automorphisms if and only if f * ( π ₁ ( D ∖ f - 1 ( f ( V f ) ) , x ) ) is a normal subgroup of π ₁ ( Ω ∖ f ( V f ) , b ) for some b ∈ Ω ∖ f ( V f ) and x ∈ f - 1 ( b ) .

Currently displaying 181 – 200 of 246