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

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

2010-02-22

arxiv.org/abs/1002.4166v1

Mathematics

Complex Variables

Scientific paper

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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