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Let $X$ be a complete variety and let $ \mathcal{L} $ be a line bundle on $X$. The following are equivalent:

1. $ \mathcal{L} $ is trivial.
2. $ \mathrm{H}^{0}(X,\mathcal{L}) \neq 0 \neq \mathrm{H}^{0}(X,\mathcal{L}^{*}) $.