DAO for curves

2023/02/06 by Zhuchao Ji, Junyi Xie, Ji, Zhuchao +1 · 3 citations
Mathematics · Physics and Astronomy · #37P05 #37P30 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2302.02583

openalex publication_date 2023/02/06 · openalex created_date 2023/02/09 · openalex updated_date 2026/07/28

Abstract

We prove the Dynamical André-Oort (DAO) conjecture proposed by Baker and DeMarco for families of rational maps parameterized by an algebraic curve. In fact, we prove a stronger result, which is a Bogomolov type generalization of DAO for curves.

Cited by

• Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture
• Polynomial endomorphisms of \A² with many periodic curves
• Global pluripotential theory for adelic line bundles

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