Every surjective self-map of a smooth rationally connected projective variety with an int-amplified endomorphism satisfies the Kawaguchi-Silverman conjecture.
Springer- Verlag, New York, 2001
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Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism
Every surjective self-map of a smooth rationally connected projective variety with an int-amplified endomorphism satisfies the Kawaguchi-Silverman conjecture.