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A characterization of proper regular mappings

T. Krasiński, S. Spodzieja (2001)

Annales Polonici Mathematici

Let X, Y be complex affine varieties and f:X → Y a regular mapping. We prove that if dim X ≥ 2 and f is closed in the Zariski topology then f is proper in the classical topology.

A note on Costara's paper

Armen Edigarian (2004)

Annales Polonici Mathematici

We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.

A Wong-Rosay type theorem for proper holomorphic self-maps

Emmanuel Opshtein (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

In this short paper, we show that the only proper holomorphic self-maps of bounded domains in k whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.

Almost Properness of Extremal Mappings

Armen Edigarian, Przemysław Kliś (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We give a simple proof of almost properness of any extremal mapping in the sense of Lempert function or in the sense of Kobayashi-Royden pseudometric.

Attracting divisors on projective algebraic varieties

Małgorzata Stawiska (2007)

Annales Polonici Mathematici

We obtain sufficient and necessary conditions (in terms of positive singular metrics on an associated line bundle) for a positive divisor D on a projective algebraic variety X to be attracting for a holomorphic map f:X → X.

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