I'm studying this article and in the second page of the second chapter I didn't understand why we can have a strict sign $\lt$ instead of less equal sign $\le$ in Clifford's theorem.
We know that the Clifford's Theorem is stated in this way:
If $l(D)\gt 0$, and $l(W-D)\gt 0$, then $l(D)\le\frac{1}{2}\deg(D)+1$
Remark: My only background is Fulton's Algebraic Curves book.
I really help.
Thanks in advance!
Clifford's theorem also tells you the cases where equality happens. These are the cases where $C$ is hyperelliptic, $D$ is canonical or $D$ is trivial. In the paper $C$ is assumed to be non-hyperelliptic and by definition of $E$, it is strictly less than a canonical divisor. So the only non-excluded case is that $E=0$, which is incorporated in the statement of the proposition.