On the density of algebraic foliations without algebraic invariant sets

DOI10.1515/CRELLE.2006.037zbMath1116.32023OpenAlexW1999578460MaRDI QIDQ5472317

Jorge Vitório Pereira, S. C. Coutinho

Publication date: 9 June 2006

Published in: Journal fur die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2006.037

zbMATH Keywords

holomorphic foliationsalgebraic invariant sets

Mathematics Subject Classification ID

Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) Singularities of holomorphic vector fields and foliations (32S65)

Related Items

Families of minimal involutive surfaces in projective space ⋮ On the construction of holomorphic foliations without invariant subvarieties of positive dimension ⋮ Pull-back components of the space of foliations of codimension ≥2 ⋮ Stability of foliations induced by rational maps ⋮ Singular foliations with trivial canonical class ⋮ Rational pullbacks of toric foliations ⋮ On the density of foliations without algebraic solutions on weighted projective planes ⋮ Invariant algebraic surfaces of polynomial vector fields in dimension three ⋮ On some foliations arising in \(\mathcal D\)-module theory ⋮ The characteristic variety of a generic foliation ⋮ On the holonomy group of algebraic curves invariant by holomorphic foliations ⋮ Foliations of multiprojective spaces and a conjecture of Bernstein and Lunts ⋮ A constructive proof of the density of algebraic Pfaff equations without algebraic solutions ⋮ On the differential simplicity of affine rings ⋮ Flags of holomorphic foliations ⋮ Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension \(3\) ⋮ Branched pull-back components of the space of codimension two foliations on ℙ4 ⋮ Generic planar algebraic vector fields are strongly minimal and disintegrated

Cites Work

• Algebraic varieties preserved by generic flows
• On Zariski problem
• On algebraic sets invariant by one-dimensional foliations on \(\mathbb{C} P(3)\)
• Irreducible components of the space of holomorphic foliations of degree two in \(\mathbb{C} P(n)\), \(n\geq 3\)
• Kodaira dimension of holomorphic singular foliations

This page was built for publication: On the density of algebraic foliations without algebraic invariant sets