A Stein Criterion Via Divisors for Domains Over Stein Manifolds - Breaz, Daniel; Vâjâitu, Viorel (MATHEMATICA SCANDINAVICA, 2014)
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,O) vanishes for i ≥ 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,O)=0 for i ≥ 1.