On the family of holomorphic mappings into projective space with lacunary hypersurfaces
type: Item
instance of: scholarly article
title: On the family of holomorphic mappings into projective space with lacunary hypersurfaces
zbMATH Open document ID: 0733.32019
author: Yukinobu Adachi
author: Masakazu Suzuki
published in: Journal of Mathematics of Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: The authors study the behavior of sequences of holomorphic mappings \(D^ k\to {\mathbb{P}}^ n\setminus A\) \((D^ k=k\)-polydisk, \({\mathbb{P}}^ n=complex\) projective n-space, \(A=hypersurface\) with \(\ell\) \((\ell \geq n+2)\) distinct irreducible components]. The following results are presented: if the ``rank'' of \(({\mathbb{P}}^ n,A)\) is n then \(\nearrow^ n\setminus A\) is tautly imbedded modulo some algebraic set B in \({\mathbb{P}}^ n\); for \(n=2\), if the number of non-hyperbolic curves in \({\mathbb{P}}^ 2\) with respect to A is finite then there is a curve S in \({\mathbb{P}}^ 2\) such that \({\mathbb{P}}^ 2\setminus A\) is tautly imbedded modulo S in \({\mathbb{P}}^ 2\). Consequences are drawn on nonhyperbolic points and on the existence of certain regular rational functions on \({\mathbb{P}}^ 2\setminus A\).
Mathematics Subject Classification ID: 32H02
zbMATH DE Number: 4212445
zbMATH Keywords: sequences of holomorphic mappings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520022
OpenAlex ID: W1541217266
DOI: 10.1215/KJM/1250520022
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description: scientific article; zbMATH DE number 4212445