A criterion for the holomorphy of the curvature of smooth planar webs and applications to dual webs of homogeneous foliations on ${\mathbb{P}}_{\mathbb{C}}^2$

Samir Bedrouni, David Marín

Let $d\ge 3$ be an integer. For a holomorphic $d$-web $\mathcal{W}$ on a complex surface $M$, smooth along an irreducible component $D$ of its discriminant $\Delta (\mathcal{W}),$ we est…