Families of automorphisms of abelian varieties

2023/09/24 by Charles Favre, Alexandra Kuznetsova, Favre, Charles +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2309.13730

Abstract

We consider some algebraic aspects of the dynamics of an automorphism on a family of polarized abelian varieties parameterized by the complex unit disk. When the action on the cohomology of the generic fiber has no cyclotomic factor, we prove that such a map can be made regular only if the family of abelian varieties does not degenerate. As a contrast, we show that families of translations are always regularizable. We further describe the closure of the orbits of such maps, inspired by results of Cantat and Amerik-Verbitsky.

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• Rational self-maps of projective surfaces with a regular iterate

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