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arXiv · 1709.05147

Divisors defined by noncritical functions

Franc Forstneric
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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.

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Franc Forstneric. 2017-09-15. Divisors defined by noncritical functions. https://doi.org/10.1090/proc/13990

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