Definition (Linearly equivalent). $D_{1}, D_{2} \in Div (E)$ are linearly equivalent if there exists $f \in \bar{K} {(E)}^{*}$ such that $div (f) = D_{1} - D_{2}$ .

Write $D_{1} \sim D_{2}$ and $[D] = {D^{'} : D^{'} \sim D}$ .