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Kawaguchi-Silverman conjecture for endomorphisms on several classes of varieties

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arxiv 1902.06072 v4 pith:BP7TIPVG submitted 2019-02-16 math.AG math.NT

Yohsuke Matsuzawa This is my paper · ORCID
classification math.AGmath.NT
keywords conjecturevarietiesendomorphismsalgebraicclasseskawaguchi-silvermanproveseveral
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We prove Kawaguchi-Silverman conjecture (KSC) and Shibata's conjecture on ample canonical heights for endomorphisms on several classes of algebraic varieties including varieties of Fano type and projective toric varieties. We also prove KSC for group endomorphisms of linear algebraic groups. We also propose a possible approach to the conjecture using equivariant MMP.

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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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