Proximity inequalities and bounds for the degree of invariant curves by foliations of ℙ_{ℂ}²

DOI10.1090/S0002-9947-97-01898-9zbMath0873.32030OpenAlexW1521065359MaRDI QIDQ4336562

Manuel M. Carnicer, Antonio Campillo

Publication date: 13 May 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01898-9

zbMATH Keywords

local invariantscomplex projective planeinvariant curves by foliationsproximity formulaereduced curve

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65)

Related Items (15)

Foliations with isolated singularities on Hirzebruch surfaces ⋮ Algebraic integrability of foliations of the plane ⋮ Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ On the Darboux integrability of polynomial differential systems ⋮ Invariants of polynomial vector fields ⋮ Local polar invariants and the Poincaré problem in the dicritical case ⋮ The Poincaré problem, algebraic integrability and dicritical divisors ⋮ The local Poincaré problem for irreducible branches ⋮ Special issue in celebration of Jack K. Hale's 70th birthday. Part 3 of 4 parts ⋮ Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\) ⋮ On the characterization of algebraically integrable plane foliations ⋮ A family of quadratic polynomial differential systems with invariant algebraic curves of arbitrarily high degree without rational first integrals ⋮ Antonio Campillo ⋮ A class of polynomial planar vector fields with polynomial first integral ⋮ Some examples for the Poincaré and Painlevé problems

Cites Work

• Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
• Topological invariants and equidesingularization for holomorphic vector fields
• Infinitely near imposed singularities and singularities of polar curves
• Invariant varieties through singularities of holomorphic vector fields
• The Poincaré problem in the nondicritical case
• Zero-Dimensional Valuation Ideals Associated with Plane Curve Branches
• Studies in Equisingularity I Equivalent Singularities of Plane Algebroid Curves
• Reduction of Singularities of the Differential Equation Ady = Bdx
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