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Cohomological q-convexity versus local q-completeness with corners

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Abstract

We show that if (D, π) is an unramified Riemann domain over a distinguished complex manifold X such that D is cohomologically q-convex, then π is locally q-complete with corners. We call X distinguished if for every point x of X there is a holomorphic line bundle \(\cal L\) on X (which may depend on x) so that the global sections \(\Gamma (X \cal L)\) of \(\cal L\) generate its 1-jets at x. Examples of distinguished complex manifolds include all complex submanifolds of Cm × Pn; in particular all Stein or projectively algebraic manifolds.

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References

  1. Andreotti, A.; Grauert, H.: Théorèmes de finitude pour la cohomologie des espaces complexes, Bull Soc. Math. France, 90 (1962), 193–259.

    MathSciNet  MATH  Google Scholar 

  2. Colţoiu, M.: A counterexample to the q-Levi problem in Pn, J. Math. Kyoto Univ., vol. 36, No. 2 (1996), 385–387.

    MathSciNet  MATH  Google Scholar 

  3. Docquier, F.; Grauert, H.: Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann., 140 (1960), 94–123.

    Article  MathSciNet  MATH  Google Scholar 

  4. Eastwood, M. G.; Vigna Suria, G.: Cohomologically complete and pseudoconvex domains, Comment. Math. Helv., 55 (1980), 413–426.

    Article  MathSciNet  MATH  Google Scholar 

  5. Fujita, O.: Domaines pseudoconvexes d’ordre général et fonctions pseudoconvexes d’ordre général, J. Math. Kyoto Univ., 30 (1990), 637–649.

    MathSciNet  MATH  Google Scholar 

  6. Lelong, P.: Domaines convexes par raport aux fonctions plurisousharmoniques, J. An. Math., 2 (1952), 178–208.

    Article  MathSciNet  MATH  Google Scholar 

  7. Matsumoto, K.: Pseudoconvex Riemann domains of general order over Stein manifolds, Mem. Fac. Sci. Kyushu Univ., Ser. A, 44 (1990), 95–109.

    MATH  Google Scholar 

  8. Peterneil, M.: Continuous q-convex exhaustion functions, Invent, math., 85(1986), 249–262.

    Article  MathSciNet  Google Scholar 

  9. Vâjâitu, V.: Some convexity properties of morphisms of complex spaces, Math. Z., 217 (1994), 215–245.

    Article  MathSciNet  MATH  Google Scholar 

  10. Vâjâitu, V.: On \(\cal P\)-complete morphisms of complex spaces, Proc. 3rd Int. Res. Inst., Hayama, 1995, Noguchi et. al eds., World Scientific Publ, Singapore (1996), 653–665.

    Google Scholar 

  11. Vâjâitu, V.: Cohomological q-convexity in projective manifolds, Kobe J. Math., 13(1996), 117–122.

    MathSciNet  MATH  Google Scholar 

  12. Vâjâitu, V.: Locally q-complete open sets in Stein spaces with isolated singularities, Kyushu J. Math., Vol. 51, No.2 (1997), 355–368.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO 70700, Bucharest, Romania

    Viorel Vâjâitu

  2. FB 7 Mathematik, Bergische Universität Wuppertal, Gauss-Str. 20, D-42097, Wuppertal, Germany

    Viorel Vâjâitu

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  1. Viorel Vâjâitu
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Correspondence to Viorel Vâjâitu.

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Vâjâitu, V. Cohomological q-convexity versus local q-completeness with corners. Results. Math. 33, 161–168 (1998). https://doi.org/10.1007/BF03322080

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