Abstract
Consider a complex one-dimensional foliation on a complex surface near a singularity $p$. If ${\mathcal{I}}$ is a closed invariant set containing the singularity $p$, then ${\mathcal{I}}$ contains either a separatrix at $p$ or an invariant real three-dimensional manifold singular at $p$.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference12 articles.
1. Incompressibilité des feuilles de germes de feuilletages holomorphes singuliers
2. The topology of normal singularities of an algebraic surface and a criterion for simplicity
3. [7] F. Loray . Pseudo-groupe d’une singularité de feuilletage holomorphe en dimension deux. Prépublication IRMAR, ccsd-00016434, 2005. Available at https://hal.archives-ouvertes.fr/hal-00016434.
4. Topology of singular holomorphic foliations along a compact divisor;Marín;J. Singul.,2014
5. Invariant Varieties Through Singularities of Holomorphic Vector Fields
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Local Invariant Hypersurfaces for Singular Foliations;Handbook of Geometry and Topology of Singularities VI: Foliations;2024
2. Topology of Singular Foliation Germs in $$\mathbb {C}^2$$;Handbook of Geometry and Topology of Singularities V: Foliations;2024
3. Characteristic curves of holomorphic foliations;Journal of Singularities;2023
4. Invariant hypersurfaces and nodal components for codimension one singular foliations;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2020-08-12
5. Meromorphic vector fields with single-valued solutions on complex surfaces;Advances in Mathematics;2019-10