The divisor $D_{\Psi}$ intersects properly the image of $\varphi_{p,H}$. The function $\Psi\circ H$ is a virtual support function on $\Sigma_{1}$ and

$$\varphi^{\ast}_{p,H}D_{\Psi}=D_{\Psi\circ H}.$$

Moreover, $\{m_{\tau}\}_{\tau\in\Sigma_{1}}$ is a set of defining vectors of $\Psi\circ H$.