The density property for Gizatullin surfaces of type $[[0,0,-r_2,-r_3]]$

Abstract

Gizatullin surfaces 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 ${\mathbb{C}}_{x,y,u,v}^4$ 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.

14 pages; changes in introduction, minor calculation error in section 5 corrected

References in corpus (3)

• Flexible varieties and automorphism groups
• Criteria for the density property of complex manifolds
• Holomorphic automorphisms of Danielewski surfaces II -- structure of the overshear group

Cited by in corpus (2)

• On automorphism groups of affine surfaces
• The density property for Gizatullin surfaces with reduced degenerate fibre