A simple example of a base point of a linear series

Question

I'm reading Fulton's algebraic curves book and he make the following definition of linear series (page 110):

Let $D$ be a divisor, and let $V$ be a subspace of $L(D)$ (as a vector space). The set of effective divisors $\{div(f)+D\mid f\in V,f\neq 0\}$ is called a linear series.

Now we can define base points: We say a point is a base point of a linear series $S$ if there is a point in the curve such that For every divisor $D\in S$ we have $P\in S$.

I'm looking for a simple example of a base point of a linear series. So, my question is this set $\{P\}$ can be considered as a linear series? if yes, we can say that $P$ is a base point of $\{P\}$.

Thanks

Answer 1

As you already defined, a linear series is a set of linearly equivalent divisors. So a set $\{P\}$ with just one point is indeed a linear series having $P$ as a base point.