Noncritical holomorphic functions on Stein spaces

作者：Forstneric Franc^*

来源：Journal of the European Mathematical Society, 2016, 18(11): 2511-2543.

DOI：10.4171/JEMS/647

• Holomorphic functions
• critical points
• Stein manifolds
• Stein spaces
• 1-convex manifolds
• stratifications

We prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, every closed discrete subset of a reduced Stein space X is the critical locus of a holomorphic function on X. We also show that for every complex analytic stratification with nonsingular strata on a reduced Stein space there exists a holomorphic function whose restriction to every stratum is noncritical. These results provide some information on critical loci of holomorphic functions on desingularizations of Stein spaces. In particular, every 1-convex manifold admits a holomorphic function that is noncritical outside the exceptional variety.

• 出版日期2016