Solution (source code)

= Solution

For every maximal cone, one endpoint of the interval of lattice points from part a realizes the corresponding Cartier datum. The toric basepoint-free criterion therefore makes $\mathcal O(kD_1)$ basepoint-free for $k\geq0$. Equivalently, part d identifies it with the pullback of the globally generated bundle $\mathcal O_{\mathbb P^1}(k)$.