Local Invariant Hypersurfaces for Singular Foliations

Felipe Cano () and Beatriz Molina-Samper ()
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Felipe Cano: Universidad de Valladolid, Dpto. Algebra, Análisis Matemático, Geometría y Topología, Facultad de Ciencias
Beatriz Molina-Samper: Universidad de Valladolid, Dpto. Algebra, Análisis Matemático, Geometría y Topología, Facultad de Ciencias, Instituto de Matemáticas de la Universidad de Valladolid

Chapter Chapter 5 in Handbook of Geometry and Topology of Singularities VI: Foliations, 2024, pp 151-199 from Springer

Abstract: Abstract The question of R. Thom of existence of invariant hypersurface for germs of holomorphic codimension one foliations is a leitmotiv in the theory. In these notes, we give a panorama of the state of art of this question, where the reduction of singularities plays a central role. We start with an elementary and detailed study of the final points expected after reduction of singularities, focusing the attention on concepts and properties concerning invariant hypersurfaces.

Date: 2024
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DOI: 10.1007/978-3-031-54172-8_5

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