Geodesic
Noncritical holomorphic functions on Stein spaces
Journal of the European Mathematical Society, Tome 18 (2016) no. 11, pp. 2511-2543

Voir la notice de l'article provenant de la source EMS Press

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 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 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.
DOI : 10.4171/jems/647
Classification : 32-XX, 57-XX, 58-XX
Keywords: Holomorphic functions, critical points, Stein manifolds, Stein spaces, 1-convex manifolds, stratifications 
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     author = {Franc Forstneri\v{c}},
     title = {Noncritical holomorphic functions on {Stein} spaces},
     journal = {Journal of the European Mathematical Society},
     pages = {2511--2543},
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     number = {11},
     year = {2016},
     doi = {10.4171/jems/647},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/647/}
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Franc Forstnerič. Noncritical holomorphic functions on Stein spaces. Journal of the European Mathematical Society, Tome 18 (2016) no. 11, pp. 2511-2543. doi: 10.4171/jems/647

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