equal to $d^2-k$.

Constructing meromorphic maps {#sec-const-mer-maps}
=============================

Let us once more describe the setting we are going to analyse. We have a curve $C$ contained in some surface $S$ with $C\cdot C= d^2$ and $d\in \mathbb N$. There exist three submersions $F$, $G$ and $H$ defined in $S$ and taking values in $\Pp^1$ which define foliations $\mathcal F$, $\mathcal G$ and $\mathcal H$ generically transversal to $C$ whose leaves are the levels curves. In order to simplify the exposition, we assume that all tangencies with $C$ are simple and distinct (when we look to the tangencies for any pair of foliations). We denote $f=F|_{C}$, $g=G|_{C}$ and $h=H|_{C}$, all of them ramification maps from $C$ to $\Pp^1$ whose ramification points correspond to the tangency points of the foliations (because $F$, $G$ and $H$ are submersions). Furthermore, we assume that $C$ embedds into $\mathbb P^2$ by a map $\phi:C\rightarrow C_0$; $C_0$ is a smooth algebraic curve of degree $d$. In order to complete the picture, we select pencil submersions $F_0$, $G_0$ and $H_0$ (with associated foliations ${\mathcal F}_0$, ${\mathcal G}_0$ and ${\mathcal H}_0$), with singular points not aligned, which restric to $C_0$ as $d$ to $1$ maps $f_0$, $g_0$ and $h_0$ 