Noncritical holomorphic functions on Stein spaces

  • Franc Forstnerič

    University of Ljubljana, Slovenia

Abstract

In this paper we prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, every closed discrete subset of a reduced Stein space XX is the critical locus of a holomorphic function on XX. We also show that for every complex analytic strati cation with nonsingular strata on a reduced Stein space there exists a holomorphic function whose restriction to every stratum is noncritical. These result 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.

Cite this article

Franc Forstnerič, Noncritical holomorphic functions on Stein spaces. J. Eur. Math. Soc. 18 (2016), no. 11, pp. 2511–2543

DOI 10.4171/JEMS/647