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Local Invariant Hypersurfaces for Singular Foliations

In: Handbook of Geometry and Topology of Singularities VI: Foliations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Felipe Cano & Beatriz Molina-Samper, 2024. "Local Invariant Hypersurfaces for Singular Foliations," Springer Books, in: Felipe Cano & José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities VI: Foliations, chapter 0, pages 151-199, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-54172-8_5
    DOI: 10.1007/978-3-031-54172-8_5
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