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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
DOI: https://doi.org/10.1090/S0002-9939-1995-1307489-2
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.


References [Enhancements On Off] (What's this?)

  • [A1] B. Aupetit, Analytic multivalued function in Banach algebras and uniform algebras, Adv. in Math. 44 (1982), 18-60. MR 654547 (84b:46059)
  • [A2] -, A primer on spectral theory, Universitext, Springer-Verlag, New York, 1991. MR 1083349 (92c:46001)
  • [A3] -, Recent trends in the field of Jordan-Banach algebras, Functional Analysis and Operator Theory, Banach Center Publications, vol. 30, Polish Academy of Sciences, Warszawa, 1994. MR 1285597 (95f:46083)
  • [A4] -, Analytic multifunctions and their applications, Proceedings "Séminaire de mathématiques supérieures" (32nd session, Université de Montréal), NATO Acad. Sci. Inst. Ser. C: Math. Phys. Sci., Kluwer Acad., Dordrecht, 1994, pp. 1-74. MR 1332958 (96d:46061)
  • [A5] -, Spectral characterization of the socle in Jordan-Banach algebras, Math. Proc. Cambridge Philos. Soc. (to appear). MR 1317491 (95m:46077)
  • [H] L. Hörmander, An introduction to complex variables, North-Holland, Amsterdam, 1973.
  • [HK] W. K. Hayman and P. B. Kennedy, Subharmonic functions, Vol. 1, Academic Press, London, 1976.
  • [R] T. J. Ransford, Interpolation and extrapolation of analytic multivalued functions, Proc. London Math. Soc. (3) 50 (1985), 480-504. MR 779400 (86e:30046)
  • [Ru] W. Rudin, Real and complex analysis, 2nd ed., McGraw-Hill, New York, 1974. MR 0344043 (49:8783)
  • [S] G. Stolzenberg, Volumes, limits and extensions of analytic varieties, Lecture Notes in Math., vol. 12, Springer-Verlag, Berlin, 1966. MR 0206337 (34:6156)
  • [T] M. Tsuji, Potential theory in modern functions theory, 2nd ed., Chelsea, New York, 1975. MR 0414898 (54:2990)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1307489-2
Article copyright: © Copyright 1995 American Mathematical Society

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