On the Danilov-Gizatullin Isomorphism Theorem

Hubert Flenner (1) , Shulim Kaliman (2) , Mikhail Zaidenberg (3)

1 Fakultät für Mathematik - Fakultät für Mathematik
2 Department of Mathematics [Miami]
3 IF - Institut Fourier

A Danilov-Gizatullin surface is a normal affine surface V=F d\S, which is a complement to an ample section S in a Hirzebruch surface Fd. By a surprising result due to Danilov and Gizatullin, [DaGi] V depends only on n=S^2 of S and neither on d nor on S. In this note we provide a new and simple proof of this Isomorphism Theorem.

Domaines: Géométrie algébrique [math.AG]

Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg. On the Danilov-Gizatullin Isomorphism Theorem. L'Enseignement Mathématique , 2009, L’ENSEIGNEMENT MATHÉMATIQUE, 55 (3/4), pp.275-283. ⟨10.4171/LEM/55-3-4⟩. ⟨hal-00318675⟩