A note on Kawaguchi-Silverman conjecture

Abstract

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.

11 pages

References in corpus (4)

• (Relative) dynamical degrees of rational maps over an algebraic closed field
• Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism
• Free abelian group actions on normal projective varieties: sub-maximal dynamical rank case
• Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties