A Stein Criterion Via Divisors for Domains Over Stein Manifolds

  • Daniel Breaz
  • Viorel Vâjâitu

Abstract

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 $i \geq 1$.
Published
2014-12-03
How to Cite
Breaz, D., & Vâjâitu, V. (2014). A Stein Criterion Via Divisors for Domains Over Stein Manifolds. MATHEMATICA SCANDINAVICA, 115(2), 287-302. https://doi.org/10.7146/math.scand.a-19226
Section
Articles