On the Arithmetic Dynamics of Monomial Maps

Lin, Jan-Li

doi:10.48550/arxiv.1704.02661

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Arithmetic Degree and Kawaguchi-silverman Conjectures1

Introduction1

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Cited by 4 publications

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“…Conjecture 2.7 is verified in several cases (not only for endomorphisms, but also for dominant rational maps). See [24,Remark 1.8], [14,19,20,22,23,29].…”

Section: Arithmetic Degree and Kawaguchi-silverman Conjecturesmentioning

confidence: 99%

Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism

Matsuzawa¹,

Yoshikawa²

2019

Preprint

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“…Conjecture 2.7 is verified in several cases (not only for endomorphisms, but also for dominant rational maps). See [24,Remark 1.8], [14,19,20,22,23,29].…”

Section: Arithmetic Degree and Kawaguchi-silverman Conjecturesmentioning

confidence: 99%

Kawaguchi-Silverman conjecture for endomorphisms on rationally connected varieties admitting an int-amplified endomorphism

Matsuzawa¹,

Yoshikawa²

2019

Preprint

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show abstract

“…In [14,Theorem 1.6], Shibata and we proved that for any surjective morphism f , there exists a point x ∈ X such that α f (x) = δ f . When X is a toric variety and f is a self-rational map on X that is induced by a group homomorphism of the algebraic torus, the set A(f ) is completely determined [18,12]. When X is quasi-projective, the arithmetic degrees and dynamical degrees can be defined by taking a smooth compactification of X.…”

Section: Introductionmentioning

confidence: 99%