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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2015 | 113 | 1 | 43-60

## Stein open subsets with analytic complements in compact complex spaces

EN

### Abstrakty

EN
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, $H^i (Y,𝓞_Y) = 0$ 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 $H⁰(X,𝓞_X(nD))$.

43-60

wydano
2015

### Twórcy

autor
• 1 University Parkway, Building F, Office F2403, Division of Science, Governors State University, University Park, IL 60484, U.S.A.