Dynamical degrees of (pseudo)-automorphisms fixing cubic hypersurfaces
Jeremy Blanc
37F1032H5014J5014E07dynamical degreepseudo-automorphismscubics
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.
Indiana University Mathematics Journal
2013
text
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10.1512/iumj.2013.62.5040
10.1512/iumj.2013.62.5040
en
Indiana Univ. Math. J. 62 (2013) 1143 - 1164
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