Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces

Abstract

We give a way to construct group of pseudo-automorphisms of rational varieties of any dimension that fix pointwise the image of a cubic hypersurface of $P^n. These group are free products of involutions, and most of their elements have dynamical degree >1. Moreover, the Picard group of the varieties obtained is not big, if the dimension is at least 3. We also answer a question of E. Bedford on the existence of birational maps of the plane that cannot be lifted to automorphisms of dynamical degree >1, even if we compose them with an automorphism of the plane.

18 pages

References in corpus (1)

• On the inertia group of elliptic curves in the Cremona group of the plane

Cited by in corpus (8)

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• On automorphisms of blowups of projective manifolds
• Infinitesimal deformations of rational surface automorphisms
• On regularizable birational maps
• The degeneration of a family of rational surface automorphisms
• Coble's question and complex dynamics of inertia groups on surfaces