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The density property for Gizatullin surfaces completed by four rational curves


Authors: Rafael B. Andrist, Frank Kutzschebauch and Pierre-Marie Poloni
Journal: Proc. Amer. Math. Soc. 145 (2017), 5097-5108
MSC (2010): Primary 14R20, 32M17; Secondary 14R10
DOI: https://doi.org/10.1090/proc/13665
Published electronically: August 30, 2017
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Abstract: Gizatullin surfaces completed by a zigzag of type $ [[0,0,-r_2,-r_3]]$ can be described by the equations $ yu=xP(x)$, $ xv=uQ(u)$ and $ yv=P(x)Q(u)$ in $ \mathbb{C}^4_{x,y,u,v}$ where $ P$ and $ Q$ are non-constant polynomials. We establish the algebraic density property for smooth Gizatullin surfaces of this type. Moreover we also prove the density property for smooth surfaces given by these equations when $ P$ and $ Q$ are holomorphic functions.


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Rafael B. Andrist
Affiliation: Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
Email: rafael.andrist@math.uni-wuppertal.de

Frank Kutzschebauch
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Email: frank.kutzschebauch@math.unibe.ch

Pierre-Marie Poloni
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
Email: pierre.poloni@math.unibe.ch

DOI: https://doi.org/10.1090/proc/13665
Received by editor(s): July 26, 2016
Received by editor(s) in revised form: January 6, 2017
Published electronically: August 30, 2017
Communicated by: Franc Forstnerič
Article copyright: © Copyright 2017 American Mathematical Society