The canonical bundle and realizable CR hypersurfaces
type: Item
instance of: scholarly article
title: The canonical bundle and realizable CR hypersurfaces
zbMATH Open document ID: 0583.32050
author: Howard Jacobowitz
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The canonical bundle of an abstract CR hypersurface \(M^{2n-1}\) is the line bundle of forms of type (n,0). If the hypersurface is realizable then this bundle has a closed non-zero section. This paper considers the converse statement. First, it is shown that this converse is false in general but does hold if M is already known to be almost realizable in that there are n-1 CR functions which are independent in a strong sense. A second result shows that not every canonical bundle has a closed section. Thus there are non-realizable CR hypersurfaces with closed sections and other non-realizable CR hypersurfaces without closed sections. The paper concludes by contrasting the \({\bar \partial}_ b\)- cohomology groups for certain non-realizable CR hypersurfaces with those of the realizable CR hypersurfaces. A related paper by the same author is ''A simple example of a non-realizable hypersurface'' which will appear in the Proc. Am. Math. Soc..
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 55R25
Mathematics Subject Classification ID: 35N15
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 18F15
zbMATH DE Number: 3933472
zbMATH Keywords: Levi operators
zbMATH Keywords: \({\bar \partial }_ b\)-complex
zbMATH Keywords: canonical bundle
zbMATH Keywords: CR hypersurface
zbMATH Keywords: CR functions
MaRDI profile type: Publication
full work available at URL: pjm.1987.127.91
OpenAlex ID: W2089071210
DOI: 10.2140/PJM.1987.127.91
description: scientific article; zbMATH DE number 3933472