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

Let $E_1$ be the invariant point divisor of ${\mathbb{P}}^1$ corresponding to the ray ${\mathbb{R}}_{\ge 0}$. Under $(u_1,u_2)\mapsto u_1$, the ray $(1,0)$ maps primitively to that ray, while no other ray maps into its interior. The toric pullback formula givesequivalently $D_1={\pi }^{-1}(E_1)$ as divisors.