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Singularities of Holomorphic Vector Fields in Dimensions ≥ 3 $$\geq 3$$ : Results and Problems

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

Author

Listed:
  • Julio Rebelo

    (Université de Toulouse, Institut de Mathématiques de Toulouse; UMR 5219)

  • Helena Reis

    (Centro de Matemática da Universidade do Porto and Faculdade de Economia da Universidade do Porto)

Abstract

In dimensions greater than or equal to 3, the local structure of a singular holomorphic foliation conceals a globally defined foliation on the projective space of dimension one less. In this paper, we will investigate how the global dynamics of the latter foliation exerts influence on several problems that apparently have a purely local nature. In the course of the discussion, a few recent results and open problems in the area will be reviewed as well.

Suggested Citation

  • Julio Rebelo & Helena Reis, 2024. "Singularities of Holomorphic Vector Fields in Dimensions ≥ 3 $$\geq 3$$ : Results and Problems," 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 39-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-54172-8_2
    DOI: 10.1007/978-3-031-54172-8_2
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