Stein open subsets with analytic complements in compact complex spaces

Jing Zhang

Annales Polonici Mathematici, Tome 113 (2015), p. 43-60 / Harvested from The Polish Digital Mathematics Library

Résumé

Let Y be an open subset of a reduced compact complex space X such that X - Y is the support of an effective divisor D. If X is a surface and D is an effective Weil divisor, we give sufficient conditions so that Y is Stein. If X is of pure dimension d ≥ 1 and X - Y is the support of an effective Cartier divisor D, we show that Y is Stein if Y contains no compact curves, $H^i (Y,_Y) = 0$ for all i > 0, and for every point x₀ ∈ X-Y there is an n ∈ ℕ such that $Φ_{|nD|}^{-1}(Φ_{|nD|}(x₀)) ∩ Y$ is empty or has dimension 0, where $Φ_{|nD|}$ is the map from X to the projective space defined by a basis of $H⁰(X,_X(nD))$.

Détail

Publié le : 2015-01-01

Zbl 1308.32013

EUDML-ID : urn:eudml:doc:280547