In viewing the tags about ample bundle with no global sections I found an example below:
If $C$ is a curve of genus $2$, and $p,q,r$ are general points on $C$, then the bundle $L=\mathcal{O}_C(p+q-r)$ is ample, but has no global sections at all.
But I don't know how to verify this? How is 'general' used here?
(Also I think it is right if we give the divisor consisting of a single point on a irrational curve. )
Let $\sigma$ be the hyperelliptic involution on $C$. Suppose that $q\ne \sigma(p)$, then I claim that $H^0(C, L)=0$ for all $r$.
Indeed, the hypothesis on $q$ implies that $L(p+q):=H^0(C, O_C(p+q))=k$ (the base field). This is a basic property of the Weierstrass points on $C$. So if $H^0(C, L)\ne 0$ for some $r$, then the inclusion $L(p+q-r)\subseteq L(p+q)$ is an equality by comparing the vector dimensions. In other words, any global section $s\in L(p+q)$ vanishes at some point of $C$, hence $s=0$ (because $s$ is constant !) and $L(p+q)=0$, contradiction.
Note that if $q=\sigma(p)$, then $p+q-r=p+\sigma(p)-r \sim \sigma(r)$, so $H^0(C, L)\cong H^0(C, O_C(\sigma(r)))\ne 0$. This explains why we need $p, q, r$ be "general". This also shows that $H^0(C, L)\ne 0$ if and only if $q=\sigma(p)$.