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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A geometrical characterization of algebraic varieties of $\textbf {C}^ 2$
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by Bernard Aupetit PDF
Proc. Amer. Math. Soc. 123 (1995), 3323-3327 Request permission

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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 3323-3327
  • MSC: Primary 32C25; Secondary 14A10
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1307489-2
  • MathSciNet review: 1307489