Polynomial vector fields with algebraic trajectories

2010/03/21 by Ferrer, Viviana, Vainsencher, Israel
#14N15 #37F75 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1003.3997

Abstract

It is known after Jouanolou that a general holomorphic foliation of degree ≥2 in projective space has no algebraic leaf. We give formulas for the degrees of the subvarieties of the parameter space of one-dimensional foliations that correspond to foliations endowed with some invariant subvariety of degree 1 or 2 and dimension ≥1.

Related

• Proper trajectories of type C* of a polynomial vector field on C2
• Holomorphic vector fields tangent to foliations in dimension three
• Limiting behavior of trajectories of complex polynomial vector fields
• Complex polynomial vector fields with many algebraic orbits
• Foliations on ℙ² with only one singular point