The density property for Gizatullin surfaces completed by four rational curves
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- by Rafael B. Andrist, Frank Kutzschebauch and Pierre-Marie Poloni PDF
- Proc. Amer. Math. Soc. 145 (2017), 5097-5108 Request permission
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.References
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Additional Information
- Rafael B. Andrist
- Affiliation: Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, D-42119 Wuppertal, Germany
- MR Author ID: 773325
- Email: rafael.andrist@math.uni-wuppertal.de
- Frank Kutzschebauch
- Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- MR Author ID: 330461
- Email: frank.kutzschebauch@math.unibe.ch
- Pierre-Marie Poloni
- Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- MR Author ID: 800101
- Email: pierre.poloni@math.unibe.ch
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5097-5108
- MSC (2010): Primary 14R20, 32M17; Secondary 14R10
- DOI: https://doi.org/10.1090/proc/13665
- MathSciNet review: 3717940