On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$

Let $\bar E$ be an irreducible plane curve over the field $\mathbf C$ of complex numbers, let $\widetilde\nu\colon\widetilde E\to E\subset\mathbf P^2$ be the normalization morphism, and let $\bar D$ be an arbitrary curve in $\mathbf P^2$ such that $\bar E\not\subset\bar D$. The main result of this paper says that if $\bar E$ and $\bar D$ intersect transversely, then $\widetilde\nu_*\colon\pi_1(\widetilde E\setminus\widetilde\nu^{-1}(\bar E\cap\bar D))\to\pi(\mathbf P^2\setminus\bar D)$ is an epimorphism.