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Holomorphic automorphisms of Danielewski surfaces I — density of the group of overshears

Authors: Frank Kutzschebauch and Andreas Lind
Journal: Proc. Amer. Math. Soc. 139 (2011), 3915-3927
MSC (2010): Primary 32Q28; Secondary 32M17
Published electronically: March 10, 2011
MathSciNet review: 2823038
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Abstract: We define the notion of shears and overshears on a Danielewski surface. We show that the group generated by shears and overshears is dense (in the compact open topology) in the path-connected component of the identity of the holomorphic automorphism group.

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Additional Information

Frank Kutzschebauch
Affiliation: Institute of Mathematics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
MR Author ID: 330461

Andreas Lind
Affiliation: Department of Mathematics, Mid Sweden University, SE-851 70 Sundsvall, Sweden

Keywords: Danielewski surfaces, holomorphic automorphisms, overshears
Received by editor(s): April 22, 2010
Received by editor(s) in revised form: April 29, 2010, and September 6, 2010
Published electronically: March 10, 2011
Communicated by: Franc Forstnerič
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.