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Moscow Mathematical Journal

Volume 16, Issue 2, April–June 2016  pp. 275–298.

Parabolic Automorphisms of Projective Surfaces (after M. H. Gizatullin)

Authors:  Julien Grivaux (1)
Author institution:(1) CNRS (Centre National de la Recherche Scientifique) Institut de mathématiques de Marseille (I2M), Université d'Aix-Marseille & Institut des hautes études scientifiques (IHÉS), Bures sur Yvette


In 1980, Gizatullin classified rational surfaces endowed with an automorphism whose action on the Neron–Severi group is parabolic: these surfaces are endowed with an elliptic fibration invariant by the automorphism. The aim of this expository paper is to present for nonexperts the details of Gizatullin’s original proof, and to provide an introduction to a recent paper by Cantat and Dolgachev.

2010 Math. Subj. Class. 14J27.

Keywords: Algebraic surface, rational surface automorphisms, Cremona group.

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