On a generalization of the Hopf fibration. III. (Subvarieties in the C- spaces)
type: Item
instance of: scholarly article
title: On a generalization of the Hopf fibration. III. (Subvarieties in the C- spaces)
zbMATH Open document ID: 0558.53034
DOI: 10.1007/BF01295153
author: Kinetsu Abe
published in: Monatshefte für Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178221
review text: [For parts I, II see Tôhoku Math. J., II. Ser. 29, 335-374 (1977; Zbl 0393.53018) and ibid. 30, 177-210 (1978; Zbl 0399.53009).] Analytic subvarieties in C-spaces are discussed. First, a certain kind of closed 2-form \(d\omega\) is constructed. Then, the subvarieties are studied by means of this 2-form. \(d\omega\) may be considered as the curvature form of a connection when C-spaces are considered as the toral bundle space over an algebraic variety. This 2-form is horizontal in its nature with respect to the bundle structure and indicates, in general, how different the bundle is from the trivial bundle. Because of this twist in the bundle space, subvarieties in C-spaces tend to inherit the same structure. In this paper, the inherited fibration structure is studied. The most concrete results are obtained when the fiber torus has complex dimension 2.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 32C25
zbMATH DE Number: 3890298
zbMATH Keywords: Analytic subvarieties
zbMATH Keywords: toral bundle
zbMATH Keywords: C-spaces
zbMATH Keywords: inherited fibration
MaRDI profile type: Publication
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OpenAlex ID: W2089344086
description: scientific article; zbMATH DE number 3890298