Finiteness and separation theorems for Dolbeault cohomologies with support conditions

• Christine Laurent-Thiébaut ^[1] ; Jürgen Leiterer ^[2]
  1. [1] Grenoble Alpes University

     Grenoble Alpes University

     Arrondissement de Grenoble, Francia

     
  2. [2] Humboldt University of Berlin

     Humboldt University of Berlin

     Berlin, Stadt, Alemania

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 3-4, 2001, págs. 565-581
• Idioma: inglés
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• Resumen

  • We consider the following situation: Let Y be an n-dimensional compact complex space whose singular part is isolated and divided into two non-empty parts Sl and S2. Set X = Y B (Sl U S2) and denote by ~, 7=1,2, the family of closed sets C c_ X such that Sj U (X B C) is a neighborhood of Sj. Using integral formulas, then we prove that, for all p, r and any holomorphic vector bundle E over X, (X, E) is Hausdorff and dim (X, E) = dim (X, E*).

    If 2 r n - 2, moreover dim (X, E) oo. The reason for this is that all ends of X are 1-concave. We study also the case when the ends of X satisfy some other convexity conditions.