Characterization of toric varieties via int-amplified endomorphisms

TL;DR

This paper characterizes toric varieties by their endomorphisms, showing that if a smooth projective variety admits an int-amplified endomorphism with certain properties, then it must be toric.

Contribution

It provides a new criterion to identify toric varieties based on the behavior of their endomorphisms and line bundles.

Findings

If $f$ is an int-amplified endomorphism, then $X$ is toric.

$f_*L$ decomposes into line bundles for all line bundles $L$ on $X$.

Characterization of toric varieties via endomorphism properties.

Abstract

In this paper, we obtain a characterization of toric varieties via int-amplified endomorphisms. We prove that if $f \colon X \to X$ is an int-amplified endomorphism of a smooth complex projective variety $X$, then $X$ is toric if and only if $f_*L$ is a direct sum of line bundles on $X$ for every line bundle $L$.