The Poincaré problem for reducible curves

DOI10.4171/rmi/1451arXiv2310.13131MaRDI QIDQ6118802

Javier Ribón, Pedro Fortuny Ayuso

Publication date: 28 February 2024

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2310.13131

zbMATH Keywords

multiplicityPoincaré problemisolated invariant curvesingularity of holomorphic foliation

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Singularities of curves, local rings (14H20) Local complex singularities (32S05)

Cites Work

• Unnamed Item
• Construction of singular holomorphic vector fields and foliations in dimension two
• On the Poincaré problem for foliations of general type
• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• Topological invariants and equidesingularization for holomorphic vector fields
• Some remarks on indices of holomorphic vector fields
• Local polar invariants and the Poincaré problem in the dicritical case
• The Poincaré problem in the nondicritical case
• The local Poincaré problem for irreducible branches
• The index of a holomorphic flow with an isolated singularity
• The Poincaré problem, algebraic integrability and dicritical divisors
• Some examples for the Poincaré and Painlevé problems
• Isolated invariant curves of a foliation
• On the Poincaré inequality for one-dimensional foliations
• Formulas for the multiplicity and the Milnor number of a foliation on \((\mathbb{C}^2,0)\)

This page was built for publication: The Poincaré problem for reducible curves