Divisors defined by noncritical functions

Forstnerič, Franc

doi:10.1090/proc/13990

Divisors defined by noncritical functions
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Proc. Amer. Math. Soc. 146 (2018), 2985-2994 Request permission

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 on $X$ which has no critical points in $X\setminus A_{\mathrm {sing}}$. A similar result is proved for complete intersections of higher codimension.

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