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On the dynamical Manin-Mumford conjecture for plane polynomial maps

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arxiv 2312.14817 v3 pith:ZE3RTITK submitted 2023-12-22 math.DS math.AGmath.NT

Romain Dujardin , Charles Favre , Matteo Ruggiero This is my paper · ORCID
classification math.DSmath.AGmath.NT
keywords conjecturedynamicalmanin-mumfordmapspolynomialavoidingcharacteristiccurves
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We prove the dynamical Manin-Mumford conjecture for regular polynomial maps of A^2 and irreducible curves avoiding super-attracting orbits at infinity, over any field of characteristic 0.

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Cited by 4 Pith papers

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

  1. Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points

    math.DS 2026-07 conditional novelty 8.0 of 10

    Any two complex polynomials either share all preperiodic points or have a uniformly bounded number of common preperiodic points, with the bound depending only on the degrees.

  2. Polynomial skew products with small relative degree

    math.DS 2025-07 accept novelty 8.0 of 10

    For a class of superattracting germs in C^2, the super-stable set W is a uniformly laminar Cantor bouquet of analytic curves, represented by integrating over curves parameterized by a non-Archimedean invariant measure.

  3. Julia sets and bifurcation loci

    math.DS 2024-11 conditional novelty 7.0 of 10

    The small Julia set of a polynomial endomorphism, the strong bifurcation locus of cubic polynomials, and the Julia set of a Hénon map are pairwise distinct in C^2.

  4. Towards Common Zeros of Iterated Morphisms

    math.AG 2024-12 conditional novelty 6.0 of 10

    Common zeros of two compositionally independent iterated morphisms are non-Zariski-dense for Henon maps, split endomorphisms of (P^1)^n, and regular polynomial skew products over number fields.

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