Year: 2026
Type: article
Abstract: 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 $$(({\mathbb {C}}^3,{\textbf{0}}),E,{\mathcal {F}})$$ ( ( C 3 , 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.
Authors: Felipe Cano, Beatriz Molina-Samper
Institution: Universidad de Valladolid
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
Award: G5655947814
OpenAlex ID: W7130824299