Polynomial vector fields with algebraic trajectories

Viviana Ferrer; Israel Vainsencher

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arXiv · 1003.3997

Polynomial vector fields with algebraic trajectories

Viviana Ferrer·Israel Vainsencher

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Abstract

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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Viviana Ferrer, Israel Vainsencher. 2010-03-21. Polynomial vector fields with algebraic trajectories. https://arxiv.org/abs/1003.3997

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