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linear system
\begin{align*} {\mathcal{L}}\in \operatorname{Pic}(X) \leadsto{\left\lvert {L} \right\rvert} \coloneqq{\mathbf{P}}H^0(X; {\mathcal{L}}) \cong \left\{{D \in \operatorname{Div}(X) {~\mathrel{\Big\vert}~}D\geq 0 \text{ and } D\sim L}\right\} \end{align*}