Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 152 / 3 / a / Solution

For $D=k{D}_1$, the lattice polytope of a toric divisor consists of $(m_1,m_2)$ satisfyingThus $m_2=0$ and $-k\le m_1\le 0$. Its lattice points index a basis of global sections, so