Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/234648
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dc.titleNon-density of points of small arithmetic degrees
dc.contributor.authorMatsuzawa, Yohsuke
dc.contributor.authorMeng, Sheng
dc.contributor.authorShibata, Takahiro
dc.contributor.authorZhang, De-Qi
dc.date.accessioned2022-11-17T01:12:58Z
dc.date.available2022-11-17T01:12:58Z
dc.date.issued2020-02-25
dc.identifier.citationMatsuzawa, Yohsuke, Meng, Sheng, Shibata, Takahiro, Zhang, De-Qi (2020-02-25). Non-density of points of small arithmetic degrees. ScholarBank@NUS Repository.
dc.identifier.urihttps://scholarbank.nus.edu.sg/handle/10635/234648
dc.description.abstractGiven a surjective endomorphism $f: X \to X$ on a projective variety over a number field, one can define the arithmetic degree $\alpha_f(x)$ of $f$ at a point $x$ in $X$. The Kawaguchi--Silverman Conjecture (KSC) predicts that any forward $f$-orbit of a point $x$ in $X$ at which the arithmetic degree $\alpha_f(x)$ is strictly smaller than the first dynamical degree $\delta_f$ of $f$ is not Zariski dense. We extend the KSC to sAND (= small Arithmetic Non-Density) Conjecture that the locus $Z_f(d)$ of all points of small arithmetic degree is not Zariski dense, and verify this sAND Conjecture for endomorphisms on projective varieties including surfaces, HyperK\"ahler varieties, abelian varieties, Mori dream spaces, simply connected smooth varieties admitting int-amplified endomorphisms, smooth threefolds admitting int-amplified endomorphisms, and some fiber spaces. We also show close relations between our sAND Conjecture and the Uniform Boundedness Conjecture of Morton and Silverman on endomorphisms of projective spaces and another long standing conjecture on Uniform Boundedness of torsion points in abelian varieties.
dc.sourceElements
dc.subjectmath.AG
dc.subjectmath.AG
dc.subjectmath.DS
dc.subjectmath.NT
dc.subjectPrimary: 37P55, Secondary: 14G05, 37B40
dc.typeArticle
dc.date.updated2022-11-16T08:13:34Z
dc.contributor.departmentMATHEMATICS
dc.published.stateUnpublished
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