Kawaguchi-Silverman conjecture is proved for all projective surfaces and for rationally connected smooth threefolds with an int-amplified endomorphism.
Int-amplified endomorphisms on normal projective surfaces
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abstract
We investigate int-amplified endomorphisms on normal projective surfaces. We prove that the output of the equivariant MMP is either a Q-abelian surface, a (equivariant) quasi-\'etale quotient of a smooth projective surface, a Mori dream space, or a projective cone of an elliptic curve.
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Kawaguchi-Silverman conjecture for certain surjective endomorphisms
Kawaguchi-Silverman conjecture is proved for all projective surfaces and for rationally connected smooth threefolds with an int-amplified endomorphism.