Geometry and Topology 2026

Positivity of compact Kahler varieties admitting an int-amplified endomorphism

In this talk, I will discuss compact Kahler varieties admitting int-amplified endomorphisms. Here, an endomorphism is called int-amplified if the pullback of some Kahler class dominates the class itself in a suitable sense. I will explain that the tangent sheaf of such a variety is pseudo-effective in a strong sense. This provides a new link between complex dynamics and positivity theory.
As an application, we prove a Kahler analogue of Yoshikawa's structure theorem: for a compact Kahler manifold admitting an int-amplified endomorphism, its Albanese map is a smooth fibration over a complex torus, and its periodic fibers are of Fano type.This is joint work with Guolei Zhong (East China Normal University).