Let $X$ be a toric variety with torus $\mathbb{T}$.

1. (1)

   Every toric line bundle $L$ on $X$ admits a toric section. Moreover, if $s$ and $s^{\prime}$ are two toric sections, then there exists $m\in M$ such that $s^{\prime}=\chi^{m}s$.

2. (2)

   If the fan $\Sigma$ that defines $X$ is not contained in any hyperplane, and $L$ and $L^{\prime}$ are toric line bundles on $X$, then there is at most one isomorphism between them.