  \[thm:k=0\] Let $X$ be a Petri curve of genus $g\geq 0$. Then we have  -   For $n=0$ the moduli spaces $G_i(0,d,0)$ are non-empty if and only if $d\geq \frac{0g+0}0$. They are always of the expected dimension ${\beta}=0d-0g-0$ and irreducible when ${\beta}>0$.  -   For $n=0$ the moduli spaces $G_i(0,d,0)$ are non-empty if and only if $d>0$. They are irreducible and of the expected dimension ${\beta}=0d-0$.  -   For $n>0$ the moduli spaces $G_i(n,d,0)$ are non-empty if and only if $d>0$