2025/11/17 by Felipe Cano, Cano, Felipe, Beatriz Molina-Samper +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2511.13474
openalex publication_date 2025/11/17 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28
Radial germs of holomorphic foliations in dimension two have a characteristic property: they are the only singular foliations whose reduction of singularities has no singular points. We also know that they are desingularized by a single dicritical blowing-up. Let us say that a foliated space ((C3, 0),E,F) is almost radial when it has a reduction of singularities without singular points; it will be "radial" under a certain additional condition on the morphism of reduction of singularities. We show that the radial condition corresponds to the "open book" situation. We end the paper with a discussion on the general almost radial case.