The density property for Gizatullin surfaces completed by four rational curves

Andrist, Rafael Benedikt; Kutzschebauch, Frank; Poloni, Pierre-Marie (2017). The density property for Gizatullin surfaces completed by four rational curves (In Press). Proceedings of the American Mathematical Society American Mathematical Society

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Abstract. Gizatullin surfaces completed by a standard zigzag of type [[0, 0, -r₂, -r₃]] can be described by the equations yu = xP(x), xv = uQ(u) and yv = P(x)Q(u) in C₄x,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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