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arXiv · 2309.13730

Families of automorphisms of abelian varieties

Charles Favre·Alexandra Kuznetsova
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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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Charles Favre, Alexandra Kuznetsova. 2023-09-24. Families of automorphisms of abelian varieties. https://arxiv.org/abs/2309.13730

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