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?