If $v_{1},\ldots v_{n}$ are first order deformation vector fields, then either $\Omega(v_{1},\ldots v_{n})=0$ everywhere on $\Sigma$, or we must have $\deg q-\deg p\geq n$, and when the equality holds then $\Omega(v_{1},\ldots v_{n})$ only vanishes at the ends with excess vanishing order zero.