article

Title: Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces

Authors: Jeremy Blanc

Issue: Volume 62 (2013), Issue 4, 1143-1164

Abstract:

$We give a way to construct groups of pseudo-au\-to\-mor\-phisms of rational varieties of any dimension that fix pointwise the image of a cubic hypersurface of $\mathbb{P}^n$. These groups 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.$