Polynomial vector fields with algebraic trajectories

Details Polynomial vector fields with algebraic trajectories Polynomial vector fields with algebraic trajectories

2010-03-21

arxiv.org/abs/1003.3997v1

Mathematics

Algebraic Geometry

16 pages, including scripts

Scientific paper

It is known after Jouanolou that a general holomorphic foliation of degree
$\geq2$ 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 $\geq1$.

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