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Geometric Convexity Properties of Coverings of 1-Convex Surfaces

  • Mihnea Colţoiu
  • Cezar JoiţaEmail author
Article
  • 11 Downloads

Abstract

We prove that a complex surface that contains an infinite Nori string of rational curves is not \(p_5\)-convex and that a covering of a 1-convex complex surface which does not contain an infinite Nori string of rational curves is \(p_5\)-convex.

Keywords

1-Convex surface Covering space Holomorphically convex space Stein space Proper modification 

Mathematics Subject Classification

32E05 32F10 32C35 32F32 

Notes

References

  1. 1.
    Bănică, C., Stănăşilă, O.: Méthodes algébriques dans la théorie globale des espaces complexes. Troisième édition. Gauthier-Villars, Paris (1977)zbMATHGoogle Scholar
  2. 2.
    Colţoiu, M.: Coverings of \(1\)-convex manifolds with \(1\)-dimensional exceptional set. Comment. Math. Helv. 68, 469–479 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Colţoiu, M., Diederich, K.: On the coverings of proper families of 1-dimensional complex spaces. Mich. Math. J. 47, 369–375 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Colţoiu, M., Joiţa, C.: The disk property of coverings of 1-convex surfaces. Proc. Am. Math. Soc. 140, 575–580 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Colţoiu, M., Joiţa, C.: Convexity properties of coverings of 1-convex surfaces. Math. Z. 275, 781–792 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Colţoiu, M., Joiţa, C.: On the separation of the cohomology of universal coverings of 1-convex surfaces. Adv. Math. 265, 362–370 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Docquier, F., Grauert, H.: Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten. Math. Ann. 140, 94–123 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Grauert, H.: On Levi’s problem and the imbedding of real-analytic manifolds. Ann. Math. 68, 460–472 (1958)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann. 146, 331–368 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Joiţa, C.: The disk property. A short survey. An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. 20, 35–42 (2012)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Laufer, H.B.: Taut two-dimensional singularities. Math. Ann. 205, 131–164 (1973)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Simion Stoilow Institute of Mathematics of the Romanian AcademyBucharestRomania

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