The density property for Gizatullin surfaces completed by four rational curves

Andrist, Rafael; Kutzschebauch, Frank; Poloni, Pierre-Marie

doi:10.1090/proc/13665

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.

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