On the characterization of algebraically integrable plane foliations

DOI10.1090/S0002-9947-10-04808-7zbMath1210.32013arXiv0812.2434OpenAlexW2102275069MaRDI QIDQ4930011

Carlos Galindo Pastor, Francisco Monserrat

Publication date: 27 September 2010

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

Full work available at URL: https://arxiv.org/abs/0812.2434

zbMATH Keywords

existence of a rational first integralnon-degenerate foliation

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65)

Related Items (4)

Foliations with isolated singularities on Hirzebruch surfaces ⋮ Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ The Poincaré problem, algebraic integrability and dicritical divisors ⋮ A class of polynomial planar vector fields with polynomial first integral

Uses Software

• SINGULAR

Cites Work

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• Algebraic integrability of foliations of the plane
• Topological types of quasihomogeneous singularities in \(\mathbb{C}^2\)
• Bounds on leaves of one-dimensional foliations
• The Poincaré problem in the nondicritical case
• Quasihomogeneous isolated singularities of hyperplanes.
• Polarity with respect ot a foliation and Cayley-Bacharach Theorems
• Some examples for the Poincaré and Painlevé problems
• Application of the theory of the discriminant to highly singular plane curves
• Proximity inequalities and bounds for the degree of invariant curves by foliations of ℙ_{ℂ}²
• Reduction of Singularities of the Differential Equation Ady = Bdx

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