Assume that $\{p_1,p_2,\ldots,p_k\}$ are $k$ points on $\mathbb{C}P^1$. Let $\chi:\pi_1(\mathbb{C}P^1\setminus  \{p_1,p_2,\ldots,p_k\})\to \mathbb{C} \setminus\{0\}$ be  a group homomorphism.

> Is there a  singular holomorphic foliation by curve, briefly SHFC,  of  $\mathbb{C}P^2$  such that $\mathbb{C}P^1 \subset \mathbb{C}P^2$ would be a leaf of  the singular  foliation(actually the leaf at infinity)having $\{p_1,p_2,\ldots,p_k\}$ as singularity of the leaf at infinity and monodoromy representation  of $\mathbb{C}P^1$ coincide $\chi$? If the answer is no, for  what representation $\chi$, the  answer is affirmative?