Holomorphy of the curvature of planar webs along an invariant curve and applications to the flatness of certain webs on ${\mathbb{P}}_{\mathbb{C}}^2$

Samir Bedrouni

Let $\mathcal{W}={\mathcal{W}}_n⊠{\mathcal{W}}_{d-n}$ be a $d$-web on $({\mathbb{C}}^2,0)$, where ${\mathcal{W}}_n$ is an $n$-web admitting an irreducible totally invariant cur…