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Convexity and Hartogs’s theorem in some open subset of a projective manifold

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Book cover Complex Analysis and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 188))

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Abstract

We study spread domains ∏: U → V over a projective manifold V = V,O (1)). First, ∏ is assumed to be a Stein morphism, e.g.a hull of meromorphy. We prove, that such a domain is an existence domain of holomorphic sections s ∈H 0 (U, E l ), where E = ∏*( O (1)). This is done by proving some line bundle convexity theorem for U. We deduce various results, e.g. a Lelong-Bremermann theorem for almost plurisubharmonic functions and a general Levi type theorem: if W is a general spread domain over V then its pseudoconvex hull is obtained from its meromorphic hull minus some hypersurface.

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References

  1. A. Andreotti, Théorème de dépendance algébrique sur les espaces complexes pseudo-concaves. Bull. Soc. Math. France 91(1963), 1–38.

    MathSciNet  MATH  Google Scholar 

  2. A. Andreotti and G. Tomassini, Some remarks on pseudoconcave manifolds, pages 85–104. Essays in topology and related topics. Mémoires dédiées à G. de Rham. Springer, 1970.

    Google Scholar 

  3. S. Asserda, The levi problem on projective manifolds. Math. Zeit. 219 (1995), 631–636.

    Article  MathSciNet  MATH  Google Scholar 

  4. W. Barth, Fortsetzung meromorpher Funktionen in Tori und komplexprojektiven Räumen. lnventiones math. 5 (1968), 42–62.

    Article  MathSciNet  MATH  Google Scholar 

  5. H.J. Bremermann, On the conjecture of the equivalence of the plurisubharmonic functions and the hartogs functions. Math. Ann. 131(1) (1956), 76–86.

    Article  MathSciNet  MATH  Google Scholar 

  6. W.L. Chow, On meromorphic maps of algebraic varieties. Annals of Maths 89 (1969), 391–403.

    Article  MATH  Google Scholar 

  7. J.P. Demailly, Estimations L2 pour l’opérateur ∂d’un fibré vectoriel holomorphe semi-positif au dessus d’une variété kählérienne complète. Ann. scient. Éc. Norm. Sup. 15(4) (1982), 457–511.

    MathSciNet  MATH  Google Scholar 

  8. J.P. Demailly, Regularization of closed positive currents and intersection theory. J. Algebraic Geometry 1 (1992), 361–409.

    MathSciNet  MATH  Google Scholar 

  9. P. Dingoyan, Un phénomène de Hartogs dans les variétés projectives. Article submitted for publication to Mathematische Zeitschrift.

    Google Scholar 

  10. P. Dingoyan, Un théorème d’Oka-Levi pour les domaines étalés au dessus de variétés projectives. To appear in Bulletin des Sciences Mathématiques.

    Google Scholar 

  11. P. Dingoyan, Fonctions méromorphes sur un ouvert localement pseudoconvexe étalé au dessus d’une variété projective. C. R. Acad. Sci. Paris 324(1) (1997), 817–822

    MathSciNet  MATH  Google Scholar 

  12. P. Dingoyan, Fonctions mésomorphes sur un espace étalé localement pseudoconvexe au dessus d’une varifé projective. Prébublication de l’Institut de Mathématiques de Jussieu, UMR 9994 du CNRS, FRANCE (130), JUIN 1997.

    Google Scholar 

  13. K. Docquier and H. Grauert, Levisches problem und Rungerscher Satz für Teilgebiete Steincher Mannigfaltigkeiten. Math. Ann. 140(1960), 94–123.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Grauert, Bemerkenswere pseudokonvexe Mannigfaltigkeiten. Math. Zeit. 81 (1963), 377–392.

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Griffiths and J. Harris, Principles of Algebraic Geometry. Wiley Classics Library. John Wiley and Sons, inc, 1 edition, 1994.

    MATH  Google Scholar 

  16. E Hartogs, Einige Folgerungen aus der Cauchyschen Integralformel bei Funktionen mehrerer Veränderlichen. Munch. Ber. 36 (1906), 223–242.

    Google Scholar 

  17. A. Hirschowitz, Pseudoconvexité au dessus d’espaces plus ou moins homogénes. Invent. Math. 26 (1974), 303–322.

    Article  MathSciNet  MATH  Google Scholar 

  18. K. Kodaira, On Kähler varieties of restricted type. Ann. of Math. 60 (1954), 28–48.

    Article  MathSciNet  MATH  Google Scholar 

  19. P. Lelong, Fonctions entières et fonctionnelles analytiques. Presse de Montréal, 1968.

    Google Scholar 

  20. E.E. Levi, Studii dui punti singolari essenziali delle funzioni analitiche di due o più variabili complesse. Annali di Math. 17(3)(1910) , 61–87.

    Article  Google Scholar 

  21. T. Napier, Convexity properties of coverings of smooth projective varieties. Math. Ann. 286(1990) , 433–479.

    Article  MathSciNet  MATH  Google Scholar 

  22. K. Oka, Sur les fonctions de plusieurs variables IX. Domaine fini sans point critique intèrieur. Jap. Jour. Math. 23 (1953), 97–155.

    MathSciNet  MATH  Google Scholar 

  23. K. R. Pinney, Line bundle convexity of pseudoconvex domains in complex manifolds. Math. Zeit. 206(1991) , 605–605.

    Google Scholar 

  24. H. Rossi, Continuation of subvarieties of projective varieties. Amer..1. Math. 91 (1969), 567–575.

    Google Scholar 

  25. H. Skoda, Morphismes surjectifs et fibrés linéaires semi-positifs. In Séminaire Pierre Lelong-Henri Skoda, volume 822 of Lecture Notes in Mathematics. Springer Verlag, 1978–79.

    Google Scholar 

  26. A. Takeuchi, Domaines pseudoconvexes sur les variétés kählériennes. J. Math. Kyoto Univ. 6 (1967), 323–357.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut de Mathèmatiques de Jussieu, Université de Paris VI, 4, Place Jussieu, 75252, Paris Cedex 05, France

    P. Dingoyan

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  1. P. Dingoyan
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Editors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie Case 247, 4, place Jussieu Cedex 05, 75252, Paris Cedex 05, France

    P. Dolbeault , A. Iordan , G. Henkin , H. Skoda  & J.-M. Trépreau , , ,  & 

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Dingoyan, P. (2000). Convexity and Hartogs’s theorem in some open subset of a projective manifold. In: Dolbeault, P., Iordan, A., Henkin, G., Skoda, H., Trépreau, JM. (eds) Complex Analysis and Geometry. Progress in Mathematics, vol 188. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8436-5_12

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  • DOI: https://doi.org/10.1007/978-3-0348-8436-5_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9566-8

  • Online ISBN: 978-3-0348-8436-5

  • eBook Packages: Springer Book Archive

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