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A geometrical characterization of algebraic varieties of $ {\bf C}\sp 2$

Author: Bernard Aupetit
Journal: Proc. Amer. Math. Soc. 123 (1995), 3323-3327
MSC: Primary 32C25; Secondary 14A10
MathSciNet review: 1307489
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Abstract: We prove that a closed subset $ V \ne {\mathbb{C}^2}$ is an algebraic variety if all its horizontal sections and its vertical sections are finite or a complex line and if $ {\mathbb{C}^2}\backslash V$ is an open set of holomorphy (equivalently pseudoconvex). This result has important consequences in the theory of the socle for Jordan-Banach algebras.

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Article copyright: © Copyright 1995 American Mathematical Society