Divisors defined by noncritical functions
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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.References
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Additional Information
- 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
- MR Author ID: 228404
- Email: franc.forstneric@fmf.uni-lj.si
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2985-2994
- MSC (2010): Primary 32C25, 32E10, 32E30, 32S20
- DOI: https://doi.org/10.1090/proc/13990
- MathSciNet review: 3787359