Stein open subsets with analytic complements in compact complex spaces

Jing Zhang. "Stein open subsets with analytic complements in compact complex spaces." Annales Polonici Mathematici 113.1 (2015): 43-60. <http://eudml.org/doc/280547>.

@article{JingZhang2015,
abstract = {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 $H⁰(X,_X(nD))$.},
author = {Jing Zhang},
journal = {Annales Polonici Mathematici},
keywords = {compact complex space; complement of the support of a divisor; Stein space},
language = {eng},
number = {1},
pages = {43-60},
title = {Stein open subsets with analytic complements in compact complex spaces},
url = {http://eudml.org/doc/280547},
volume = {113},
year = {2015},
}

TY - JOUR
AU - Jing Zhang
TI - Stein open subsets with analytic complements in compact complex spaces
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 1
SP - 43
EP - 60
AB - 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 $H⁰(X,_X(nD))$.
LA - eng
KW - compact complex space; complement of the support of a divisor; Stein space
UR - http://eudml.org/doc/280547
ER -