Let $X$ be a complete non-singular curve and $\Omega^1$ the sheaf of regular 1-forms on $X$. Let $g=\dim H^0(X, \Omega^1)$ the genus of $X$. I've read that there are $g$ points $P_1,\cdots, P_g$ on $X$ such that if $D=\sum_{i=1}^{g} P_i$,
$\dim H^0(X, \Omega^1\otimes \mathcal{O}_X(-D))=0$.
Here, $\mathcal{O}_X(-D)$ is the associated sheaf to the divisor $D$ on $X$.
I don't understand why this divisor exists.