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Dynamics of Endomorphisms for Projective Bundles on Elliptic Curves

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arxiv 2310.03313 v2 pith:TZP37H6U submitted 2023-10-05 math.AG

Brett Nasserden , Sasha Zotine This is my paper · ORCID
classification math.AG
keywords bundlesprojectivecurvesconjectureellipticdynamicsendomorphismsprove
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We study the dynamics of surjective endomorphisms of projective bundles on elliptic curves and relate their dynamical properties to the geometry of the bundle. As an application we prove the Kawaguchi--Silverman conjecture for projective bundles on elliptic curves, thereby completing the conjecture for all projective bundles on curves. Our approach is to use the transition functions of the bundles. This allows us to further prove the conjecture for projective split bundles on a smooth projective variety with finitely generated Mori cone.

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  1. Dynamical Iitaka theory on Fano contractions

    math.AG 2025-06 conditional novelty 7.0 of 10

    The Kawaguchi-Silverman conjecture is proved for projective bundles over abelian varieties or smooth projective varieties of Picard number one, via new structure theorems for endomorphisms of Fano contractions.

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