无常变体上的自形族

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-07-23 DOI:10.1007/s00208-024-02943-4

Charles Favre, Alexandra Kuznetsova

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引用次数: 0

摘要

我们考虑了以复数单位盘为参数的极化无性变体族上的自变态动力学的一些代数问题。当对泛纤维同调的作用没有旋回因子时，我们证明只有当无性变体族不退化时，这种映射才能正则化。作为对比，我们证明了平移族总是可规则化的。受康塔特（Cantat）和阿梅里克-韦尔比茨基（Amerik-Verbitsky）结果的启发，我们进一步描述了这类映射轨道的闭合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Families of automorphisms on abelian varieties

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Families of automorphisms on abelian varieties

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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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.