On the Poincaré inequality for one-dimensional foliations

DOI10.1112/S0010437X05001764zbMath1097.32010OpenAlexW2138633056MaRDI QIDQ5475427

Daniel Lehmann, Vincent Cavalier

Publication date: 19 June 2006

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0010437x05001764

zbMATH Keywords

Poincaré inequalitygenus formulaGSV-indexdegree of an algebraic foliation

Mathematics Subject Classification ID

Complete intersections (14M10) Global theory of complex singularities; cohomological properties (32S20) Singularities of holomorphic vector fields and foliations (32S65) Relations of (K)-theory with cohomology theories (19E20)

Related Items (11)

Foliations with isolated singularities on Hirzebruch surfaces ⋮ Bounds for sectional genera of varieties invariant under Pfaff fields ⋮ Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ The Poincaré problem for reducible curves ⋮ Invariant algebraic surfaces of polynomial vector fields in dimension three ⋮ GSV-index for holomorphic Pfaff systems ⋮ 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 ⋮ Degree of an algebraic solution of a \(d\)-web in the complex projective plane ⋮ A class of polynomial planar vector fields with polynomial first integral

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