Stein open subsets with analytic complements in compact complex spaces

• Autorzy: Jing Zhang
• Języki publikacji: 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 $H⁰(X,𝓞_X(nD))$.

Kategorie tematyczne

• 14E05: Rational and birational maps
• 32E10: Stein spaces, Stein manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 113
• Numer: 1
• Strony: 43-60

Daty

wydano

2015

Twórcy

autor

Jing Zhang

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

Identyfikatory

DOI

10.4064/ap113-1-2