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## Trivial Line Bundle

Algebraic Geometry
Tsakanikas Nickos
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### Trivial Line Bundle

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