Value distribution of meromorphic mappings into compactified locally symmetric spaces
type: Item
instance of: scholarly article
title: Value distribution of meromorphic mappings into compactified locally symmetric spaces
zbMATH Open document ID: 0760.32013
author: Yoshihiro Aihara
author: Junjiro Noguchi
published in: Kodai Mathematical Journal
publication date: 1992-09-26T00:00:00Z
review text: We quote from the introduction: ``There have been many works to generalize the Nevanlinna theory (especially his Second Main Theorem) to the higher dimensional case. While the so-called equidimensional holomorphic or meromorphic mappings \(f:W\to V\) between algebraic varieties have been well studied, we do not know very much about \(f:W\to V\) with \(\dim W<\dim V\). So far, we have to put some special restriction on target spaces or on the divisors of the target spaces. In this paper, we will establish an inequality of the Second Main Theorem type for meromorphic mappings into a compactification of a locally symmetric space.'' This ``Second Main Theorem'' is used in a subsequent paper by the authors [the first author, Kodai Math. J. 14, No. 3, 392-405 (1991; see the paper above)] to prove unicity theorems for meromorphic mappings of a finite analytic covering space over \(\mathbb{C}^ n\) into a smooth toroidal compactification of a locally symmetric space.
Mathematics Subject Classification ID: 32H30
Mathematics Subject Classification ID: 32M99
zbMATH DE Number: 55867
zbMATH Keywords: higher dimensional
zbMATH Keywords: Nevanlinna theory
zbMATH Keywords: Second Main Theorem
zbMATH Keywords: locally symmetric spaces
reviewed by: Emil J. Straube
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039457
OpenAlex ID: W2031991159
cites work: Q4099744
cites work: Curvature operator of the Bergman metric on a homogeneous bounded domain
cites work: Some metric properties of arithmetic quotients o f symmetric spaces and an extension theorem
cites work: Holomorphic bisectional curvature
cites work: Nevanlinna theory and holomorphic mappings between algebraic varieties
cites work: Extensions of Holomorphic Maps
cites work: Q5608188
cites work: Satake compactification and the great Picard theorem
cites work: Generalization of the big Picard theorem
cites work: Hirzebruch's proportionality theorem in the non-compact case
cites work: The nonexistence of certain level structures on abelian varieties over complex function fields
cites work: Meromorphic mappings of a covering space over \(\mathbb{C}^m\) into a projective variety and defect relations
cites work: Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties
cites work: On the value distribution of meromorphic mappings of covering spaces over \({\mathbb{C}}^ m\) into algebraic varieties
cites work: Moduli spaces of holomorphic mappings into hyperbolically imbedding complex spaces and locally symmetric spaces
cites work: MODULI SPACE OF ABELIAN VARIETIES WITH LEVEL STRUCTURE OVER FUNCTION FIELDS
cites work: Q3997733
cites work: Defect relations and ramification
cites work: Nevanlinna defect relations for singular divisors
cites work: Defect relations for holomorphic maps between spaces of different dimensions
cites work: Q4153016
DOI: 10.2996/KMJ/1138039457
description: scientific article; zbMATH DE number 55867