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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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On the compactification of strongly pseudoconvex surfaces
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by Vo Van Tan PDF
Proc. Amer. Math. Soc. 82 (1981), 407-410 Request permission

Abstract:

In this paper, we shall prove that the compactification of a strongly pseudoconvex surface is either a projective algebraic or an Inoue surface. Furthermore, we shall construct an example of a strongly pseudoconvex surface $X$ which admits two distinct compactifications: One $M’$ projective algebraic and the other one $M$ (highly) nonalgebraic.
References
  • Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
  • Alan Howard, On the compactification of a Stein surface, Math. Ann. 176 (1968), 221–224. MR 223602, DOI 10.1007/BF02052827
  • Masahisa Inoue, New surfaces with no meromorphic functions, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp.Β 423–426. MR 0442296
    • K. Kodaira, Collected works. Vols. I, III, Princeton Univ. Press, Princeton, N. J., 1975. Vo Van Tan, On the classification of $q$-convex complex spaces by their compact analytic subvarieties, Ph.D. Thesis, Brandeis University, Waltham, Mass., 1974.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 82 (1981), 407-410
  • MSC: Primary 32J05; Secondary 32F30
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0612730-5
  • MathSciNet review: 612730