TY - JOUR AU - Breaz, Daniel AU - Vâjâitu, Viorel PY - 2014/12/03 Y2 - 2024/03/28 TI - A Stein Criterion Via Divisors for Domains Over Stein Manifolds JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 115 IS - 2 SE - Articles DO - 10.7146/math.scand.a-19226 UR - https://www.mscand.dk/article/view/19226 SP - 287-302 AB - 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 $i \geq 1$. ER -