# Stein open subsets with analytic complements in compact complex spaces

Annales Polonici Mathematici (2015)

- Volume: 113, Issue: 1, page 43-60
- ISSN: 0066-2216

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topJing 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 -

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