Kawaguchi–Silverman conjecture on automorphisms of projective threefolds

Abstract

Under the framework of dynamics on normal projective varieties by Kawamata, Nakayama and Zhang, and Hu and Li, we may reduce Kawaguchi–Silverman conjecture for automorphisms [Formula: see text] on normal projective threefolds [Formula: see text] with either the canonical divisor [Formula: see text] is trivial or negative Kodaira dimension to the following two cases: (i) [Formula: see text] is a primitively automorphism of a weak Calabi–Yau threefold, (ii) [Formula: see text] is a rationally connected threefold. And we prove Kawaguchi–Silverman conjecture is true for automorphisms of normal projective varieties [Formula: see text] with the irregularity [Formula: see text]. Finally, we discuss Kawaguchi–Silverman conjecture on normal projective varieties with Picard number two.