The Poincaré problem, algebraic integrability and dicritical divisors

DOI10.1016/j.jde.2014.02.015zbMath1297.14012arXiv1110.2973OpenAlexW2064899357MaRDI QIDQ2442906

Francisco Monserrat, Carlos Galindo Pastor

Publication date: 2 April 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2973

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Singularities of holomorphic vector fields and foliations (32S65) Foliations in differential topology; geometric theory (57R30) Divisors, linear systems, invertible sheaves (14C20) Moduli, classification: analytic theory; relations with modular forms (14J15) Ordinary differential equations on complex manifolds (34M45)

Related Items (10)

Foliations with isolated singularities on Hirzebruch surfaces ⋮ Poincaré problem for weighted projective foliations ⋮ The Poincaré problem for foliations on compact toric orbifolds ⋮ Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ The Poincaré problem for reducible curves ⋮ Local polar invariants and the Poincaré problem in the dicritical case ⋮ The local Poincaré problem for irreducible branches ⋮ On the computation of Darboux first integrals of a class of planar polynomial vector fields ⋮ Catching Tangent Curves in Fields of Lines ⋮ A class of polynomial planar vector fields with polynomial first integral

Uses Software

• Mathematica

Cites Work

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