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15 January 2013 Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space
Frank Kutzschebauch, Sam Lodin
Duke Math. J. 162(1): 49-94 (15 January 2013). DOI: 10.1215/00127094-1958969

Abstract

We construct holomorphic families of proper holomorphic embeddings of Ck into Cn (0<k<n1), so that for any two different parameters in the family, no holomorphic automorphism of Cn 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 Cn, we derive the existence of families of holomorphic C-actions on Cn (n5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of C-actions on Cn (with prescribed linear part at a fixed point).

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Frank Kutzschebauch. Sam Lodin. "Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space." Duke Math. J. 162 (1) 49 - 94, 15 January 2013. https://doi.org/10.1215/00127094-1958969

Information

Published: 15 January 2013
First available in Project Euclid: 14 January 2013

zbMATH: 1266.32029
MathSciNet: MR3011872
Digital Object Identifier: 10.1215/00127094-1958969

Subjects:
Primary: 32H02 , 32M05
Secondary: 32Q28 , 32Q40 , 32Q45

Rights: Copyright © 2013 Duke University Press

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Vol.162 • No. 1 • 15 January 2013
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