On the Danilov-Gizatullin Isomorphism Theorem

Hubert Flenner; Shulim Kaliman; Mikhail Zaidenberg

doi:10.4171/lem/55-3-4

JournalslemVol. 55, No. 3/4pp. 275–283

On the Danilov-Gizatullin Isomorphism Theorem

Hubert Flenner
Ruhr-Universität Bochum, Germany
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Shulim Kaliman
University of Miami, Coral Gables, USA
- MathSciNet
- zbMATH Open
Mikhail Zaidenberg
Université Grenoble I, Saint-Martin-D'hères, France
- MathSciNet
- zbMATH Open

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Abstract

A Danilov–Gizatullin surface is a normal affine surface $V = Σ_{d} ∖ S$ , which is a complement to an ample section $S$ in a Hirzebruch surface $Σ_{d}$ . By a surprising result due to Danilov and Gizatullin [DaGi], $V$ depends only on $n = S^{2}$ and neither on $d$ nor on $S$ . 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