On the Danilov-Gizatullin Isomorphism Theorem

  • Hubert Flenner

    Ruhr-Universität Bochum, Germany
  • Shulim Kaliman

    University of Miami, Coral Gables, USA
  • Mikhail Zaidenberg

    Université Grenoble I, Saint-Martin-D'hères, France


A {\it Danilov-Gizatullin surface} is a normal affine surface V=ΣdSV=\Sigma_d\setminus S, which is a complement to an ample section SS in a Hirzebruch surface Σd\Sigma_d. By a surprising result due to Danilov and Gizatullin [DaGi], VV depends only on n=S2n=S^2 and neither on dd nor on SS. In this note we provide a new and simple proof of this Isomorphism Theorem.

Cite this article

Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg, On the Danilov-Gizatullin Isomorphism Theorem. Enseign. Math. 55 (2009), no. 3/4, pp. 275–283

DOI 10.4171/LEM/55-3-4