  We collect some results on endomorphisms on projective varieties related with
the Kawaguchi-Silverman conjecture. We discuss certain condition on
automorphism groups of projective varieties and positivity conditions on
leading real eigendivisors of self-morphisms. We prove Kawaguchi-Silverman
conjecture for endomorphisms on projective bundles on a smooth Fano variety of
Picard number one. In the last section, we discuss endomorphisms and augmented
base loci of their eigendivisors.
