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