Divisors defined by noncritical functions

Abstract

In this paper we show that every complex hypersurface $A$ in a Stein manifold $X$ with $H^2(X;\mathbb{Z})=0$ is the divisor of a holomorphic function $f$ on $X$ whose critical points are precisely the singular points of $A$. A similar result is proved for complete intersections of higher codimension.

References in corpus (2)

• Noncritical holomorphic functions on Stein spaces
• Gunning-Narasimhan's theorem with a growth condition