Endomorphisms of the plane preserving a pencil of curves

2007/03/02 by Marius Dabija, Mattias Jonsson, Dabija, Marius +2 · 1 citation
Mathematics · #14C21 #32H50 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #math.DS #msc:14C21 #msc:32H50

paper · pdf · doi:10.48550/arxiv.math/0703050

5 pages. To appear in Internat. J. Math

arxiv created 2007/03/02 · openalex publication_date 2007/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify endomorphisms of the plane that preserve a pencil of curves.

Cited by

• Polynomial endomorphisms of \A² with many periodic curves

Related

• Endomorphisms of hypersurfaces and other manifolds
• Endomorphisms of the projective plane and the image of the Suslin-Hurewicz map
• Pencils of plane curves and characteristic varieties
• Birational conjugacies between endomorphisms on the projective plane
• The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane