Kawaguchi-Silverman conjecture is proved for all projective surfaces and for rationally connected smooth threefolds with an int-amplified endomorphism.
Dynamical Degree and Arithmetic Degree of Endomorphisms on Product Varieties
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abstract
For a dominant rational self-map on a smooth projective variety defined over a number field, Shu Kawaguchi and Joseph H. Silverman conjectured that the dynamical degree is equal to the arithmetic degree at a rational point whose forward orbit is well-defined and Zariski dense. We give some examples of self-maps on product varieties and rational points on them for which the Kawaguchi-Silverman conjecture holds.
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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.