On the density of Second Order Differential Equations without algebraic solutions on $\mathbb{P}}^{2}$

preprint2010arXivOpen access

We prove that a generic second order differential equation in the projective plane has no algebraic solutions when the bidegree is big enough. We also proof an analogous result for webs on $\mathbb{P}}^{2}$.

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On the density of Second Order Differential Equations without algebraic solutions on $\mathbb{P}}^{2}$

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