Work

The arithmetic of polynomial dynamical pairs

Year: 2020

Type: preprint

Abstract: We study one-dimensional algebraic families of pairs given by a polynomial with a marked point. We prove an "unlikely intersection" statement for such pairs thereby exhibiting strong rigidity features for these pairs. We infer from this result the dynamical André-Oort conjecture for curves in the moduli space of polynomials, by describing one-dimensional families in this parameter space containing infinitely many post-critically finite parameters.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2004.13801

Authors: Favre, Charles, Gauthier, Thomas

Institutions: Centre National de la Recherche Scientifique, École Polytechnique, Centre de Mathématiques Laurent Schwartz, Institut Polytechnique de Paris, University of British Columbia, Pacific Institute for the Mathematical Sciences

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Awards: New points of view in rational dynamics in several variables, G6803667113

OpenAlex ID: W4287811160

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