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On the compactification of strongly pseudoconvex surfaces


Author: Vo Van Tan
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
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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 [Enhancements On Off] (What's this?)

  • [1] Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 0137127, https://doi.org/10.1007/BF01441136
  • [2] Alan Howard, On the compactification of a Stein surface, Math. Ann. 176 (1968), 221–224. MR 0223602, https://doi.org/10.1007/BF02052827
  • [3] 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. 423–426. MR 0442296
  • [4] K. Kodaira, Collected works. Vols. I, III, Princeton Univ. Press, Princeton, N. J., 1975.
  • [5] 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

DOI: https://doi.org/10.1090/S0002-9939-1981-0612730-5
Keywords: Classification of compact $ {\mathbf{C}}$-analytic surfaces, exceptional curves of the first kind, minimal surfaces, Inoue surfaces, ruled surfaces, strongly pseudoconvex surfaces
Article copyright: © Copyright 1981 American Mathematical Society

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