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Unlikely intersections problem for automorphisms of Markov surfaces

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arxiv 2401.05762 v4 pith:KX5UQUC5 submitted 2024-01-11 math.AG math.DSmath.GTmath.NT

classification math.AGmath.DSmath.GTmath.NT
keywords automorphismsentropyintersectionsmarkovpositiveproblemsharesurfaces
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We study the problem of unlikely intersections for automorphisms of Markov surfaces of positive entropy. We show for certain parameters that two automorphisms with positive entropy share a Zariski dense set of periodic points if and only if they share a common iterate. Our proof uses arithmetic equidistribution for adelic line bundles over quasiprojective varieties, the theory of laminar currents and quasi-Fuchsian representation theory.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Open surfaces with a triangle at infinity

    math.AG 2026-07 accept novelty 7.0 of 10

    Triangle surfaces are exactly the Markov-type cubics xyz=x^2+y^2+z^2+ax+by+cz+d, and their automorphism groups are Gσ⋊Γ with Γ one of five finite groups from Table 1.

  2. Global pluripotential theory for adelic line bundles

    math.AG 2025-07 conditional novelty 6.0 of 10

    The category of strongly semiample adelic line bundles on a quasi-projective arithmetic variety is equivalent to line bundles on its Berkovich analytification with norm-equivariant continuous semipositive metrics.

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