Weak hyperbolicity and many-dimensional analogues of Picard's theorem
type: Item
instance of: scholarly article
title: Weak hyperbolicity and many-dimensional analogues of Picard's theorem
zbMATH Open document ID: 0729.32011
DOI: 10.1007/BF00970169
author: M. A. Chinak
published in: Siberian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: The author studies holomorphic mappings between complex manifolds omitting analytic subsets of the target manifold. The main result of the present paper is the following theorem: Let M be an n-dimensional compact complex manifold, \(D\subset M\) a closed analytic hypersurface with normal crossings, and N a complex manifold of dimension \(n-1.\) If \(c_ 1(D)+c_ 1(K_ M)\geq 0,\) then every holomorphic mapping f: \(N\times {\mathbb{C}}\to M\) without essential singularities at infinity, i.e. which extends to a meromorphic mapping f: \(N\times {\bar {\mathbb{C}}}\to M\), is everywhere degenerate. The proof involves some results concerning weakly hyperbolic manifolds - a notion introduced and studied by the author [Sib. Math. J. 29, No.1, 161-163 (1988); translation from Sib. Math. Zh. 29, No.1(167), 209-212 (1988; Zbl 0638.32023)]. The author's theorem generalizes an analogous result in the Griffiths- Carlson-King theory known under the stronger condition \(c_ 1(D)+c_ 1(K_ M)>0\) [\textit{Ph. Griffiths} and \textit{J. King}, Acta Math. 130, 145- 220 (1973; Zbl 0258.32009)].
Mathematics Subject Classification ID: 32H25
Mathematics Subject Classification ID: 32Q45
zbMATH DE Number: 4204792
reviewed by: Johann Davidov
MaRDI profile type: Publication
cites work: Nevanlinna theory and holomorphic mappings between algebraic varieties
cites work: Intrinsic distances, measures and geometric function theory
cites work: Q5608188
cites work: Q3322392
cites work: Q4195061
cites work: Q5521609
full work available at URL: https://doi.org/10.1007/bf00970169
OpenAlex ID: W2041316080
description: scientific article; zbMATH DE number 4204792