Polynomial vector fields with algebraic trajectories
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.
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