Holomorphic self-maps of singular rational surfaces

2008/09/10 by Charles Favre, Favre, Charles
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AG #math.DS

paper · pdf · doi:10.48550/arxiv.0809.1724

37 pages. To appear in Publicacions Matematiques.

openalex publication_date 2008/09/10 · arxiv created 2010/03/15 · arxiv updated 2010/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof of the classification of normal singular surface germs admitting non-invertible holomorphic self-maps and due to J. Wahl. We then draw an analogy between the birational classification of singular holomorphic foliations on surfaces, and the dynamics of holomorphic maps. Following this analogy, we introduce the notion of minimal holomorphic model for holomorphic maps. We give sufficient conditions which ensure the uniqueness of such a model.

Citations

• Entropy of meromorphic maps and dynamics of birational maps
• Dynamique des automorphismes des surfaces K3

Related

• Local dynamics of non-invertible maps near normal surface singularities
• Nondegenerate germs of holomorphic foliations with prescribed holonomy
• The Classification of Surfaces
• Index theorems for meromorphic self-maps of the projective space
• Foliations invariant by rational maps