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Proceedings of the American Mathematical Society

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Divisors defined by noncritical functions


Author: Franc Forstnerič
Journal: Proc. Amer. Math. Soc. 146 (2018), 2985-2994
MSC (2010): Primary 32C25, 32E10, 32E30, 32S20
DOI: https://doi.org/10.1090/proc/13990
Published electronically: March 9, 2018
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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 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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Franc Forstnerič
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI–1000 Ljubljana, Slovenia —and— Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI–1000 Ljubljana, Slovenia
Email: franc.forstneric@fmf.uni-lj.si

DOI: https://doi.org/10.1090/proc/13990
Keywords: Stein manifold, divisor, noncritical function, complete intersection
Received by editor(s): September 19, 2017
Received by editor(s) in revised form: September 23, 2017
Published electronically: March 9, 2018
Communicated by: Filippo Bracci
Article copyright: © Copyright 2018 American Mathematical Society

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