Characterization of toric varieties via int-amplified endomorphisms

Abstract

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

8 pages