Kutzschebauch, Frank; Lodin, Sam (2013). Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space. Duke Mathematical Journal, 162(1), pp. 4994. Duke University Press 10.1215/001270941958969

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We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the longstanding holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).
Item Type: 
Journal Article (Original Article) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 
UniBE Contributor: 
Kutzschebauch, Frank 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
00127094 
Publisher: 
Duke University Press 
Language: 
English 
Submitter: 
Mario Amrein 
Date Deposited: 
28 Feb 2014 09:48 
Last Modified: 
04 May 2015 14:20 
Publisher DOI: 
10.1215/001270941958969 
BORIS DOI: 
10.7892/boris.41922 
URI: 
https://boris.unibe.ch/id/eprint/41922 