Linear equivalence of divisors

Two divisors $D$ and $E$ are linearly equivalent, written $D\sim E$, when $D-E$ is a principal divisor. Multiplication by a rational function whose divisor is $D-E$ gives an isomorphism between their spaces of sections, so $\ell (D)=\ell (E)$.

A divisor class is an equivalence class of divisors under linear equivalence. Degree descends to divisor classes because every principal divisor has degree zero.