A Stein Criterion Via Divisors for Domains Over Stein Manifolds
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It is shown that a domain $X$ over a Stein manifold is Stein if the following two conditions are fulfilled: a) the cohomology group $H^i(X,\mathscr{O})$ vanishes for $i \geq 2$ and b) every topologically trivial holomorphic line bundle over $X$ admits a non-trivial meromorphic section. As a consequence we recover, with a different proof, a known result due to Siu stating that a domain $X$ over a Stein manifold $Y$ is Stein provided that $H^i(X,\mathscr{O})=0$ for $i \geq 1$.
2004 ◽
Vol 15
(08)
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pp. 735-747
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2010 ◽
Vol 21
(04)
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pp. 497-522
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2007 ◽
Vol 143
(6)
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pp. 1576-1592
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2003 ◽
Vol 14
(02)
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pp. 191-209
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