Let $C$ be a nonsingular curve. In the proof of Theorem(V.2.17) of hartshorne book, I see the following statment:
We have only to take maps $\mathcal{O} \rightarrow \mathcal{O}(-e)$ and $\mathcal{O}(n-e) \rightarrow \mathcal{O}(n-e)$ corresponding to effective divisors of degrees $n-e$ and $n$ on $C$ which do not meet. Then the corresponding map $\mathcal{O}\oplus \mathcal{O}(-e) \rightarrow \mathcal{O}(n-e) $ is be surjective.
My questions is that how define the above maps? and why last map is surjective?