Linear equivalence of Cartier divisors ($D\sim E$)

Two Cartier divisors are linearly equivalent when their difference is a principal Cartier divisor. Their associated line bundles are then isomorphic, so their global section spaces have the same dimension. This definition works in every dimension.

A principal Cartier divisor is represented on every chart by the same nonzero rational function. It is linearly equivalent to zero and has zero intersection number with every complete curve.