Resumen de Finiteness and separation theorems for Dolbeault cohomologies with support conditions

Christine Laurent-Thiébaut, Jürgen Leiterer

• 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.