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Dynamical Degree and Arithmetic Degree of Endomorphisms on Product Varieties

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arxiv 1604.04174 v3 pith:IN4U7P5T submitted 2016-04-14 math.NT math.AGmath.DS

Kaoru Sano This is my paper · ORCID
classification math.NTmath.AGmath.DS
keywords degreerationalarithmeticdynamicalproductvarietiesconjectureconjectured
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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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  1. Kawaguchi-Silverman conjecture for certain surjective endomorphisms

    math.AG 2019-08 accept novelty 8.0 of 10

    Kawaguchi-Silverman conjecture is proved for all projective surfaces and for rationally connected smooth threefolds with an int-amplified endomorphism.

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