Families of automorphisms of abelian varieties

Author:

Charles Favre, Alexandra Kuznetsova

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Dynamical Systems (math.DS)

journal:

date:

2023-09-23 16:00:00

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.

PDF: Families of automorphisms of abelian varieties.pdf