Tohoku Mathematical Journal
2020
March
SECOND SERIES VOL. 72, NO. 1

Tohoku Math. J.
72 (2020), 1-13

Title DYNAMICAL DEGREE AND ARITHMETIC DEGREE OF ENDOMORPHISMS ON PRODUCT VARIETIES

Author Kaoru Sano

(Received January 5, 2017, revised October 19, 2017)
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 (first) dynamical degree is equal to the arithmetic degree at an algebraic 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.

Mathematics Subject Classification. Primary 37P55; Secondary 11G50.
Key words and phrases. Erithmetic degrees, dynamical degrees, height functions.

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