TY - JOUR
T1 - Analyticity of compact complements of complete kähler manifolds
AU - Anchouche, Boudjemâa
PY - 2009/9
Y1 - 2009/9
N2 - Let X be a Stein manifold, dimC X ≥ 2, K a compact subset of X, and ω an open subset of X containing K such that ω\K is connected. Suppose that ω\K carries a complete Kähler metric of bounded bisectional curvature, and locally of finite volume near K. If K admits a Stein neighborhood V, V. ω, such that V/K is connected and H2 (V,R) = 0, then K is a complex analytic subvariety of X, hence reduced to a finite number of points.
AB - Let X be a Stein manifold, dimC X ≥ 2, K a compact subset of X, and ω an open subset of X containing K such that ω\K is connected. Suppose that ω\K carries a complete Kähler metric of bounded bisectional curvature, and locally of finite volume near K. If K admits a Stein neighborhood V, V. ω, such that V/K is connected and H2 (V,R) = 0, then K is a complex analytic subvariety of X, hence reduced to a finite number of points.
KW - Analyticity of compact sets
KW - Complete Kähler metrics
KW - Stein manifolds
UR - http://www.scopus.com/inward/record.url?scp=77951066358&partnerID=8YFLogxK
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U2 - 10.1090/S0002-9939-09-09762-7
DO - 10.1090/S0002-9939-09-09762-7
M3 - Article
AN - SCOPUS:77951066358
SN - 0002-9939
VL - 137
SP - 3037
EP - 3044
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -