A characterization of compact complex tori via automorphism groups

TL;DR

This paper characterizes compact complex tori among Kaehler manifolds by analyzing the size of their automorphism groups, with implications for complex dynamics.

Contribution

It provides a new criterion for identifying complex tori based on the structure of their automorphism groups, extending previous classifications.

Findings

A compact Kaehler manifold is a complex torus if its automorphism group has infinite continuous and discrete parts, unless it admits a non-trivial G-equivariant fibration.

The paper offers applications of this characterization to complex dynamics.

It clarifies the relationship between automorphism group properties and the geometric structure of the manifold.

Abstract

We show that a compact Kaehler manifold X is a complex torus if both the continuous part and discrete part of some automorphism group G of X are infinite groups, unless X is bimeromorphic to a non-trivial G-equivariant fibration. Some applications to dynamics are given.