Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 152 / 2 / a / i

The product fan for ${\mathbb{P}}^1\times {\mathbb{A}}^1$ has rays generated byand maximal cones $\mathrm{Cone}(e_1,e_2)$ and $\mathrm{Cone}(e_2,-e_1)$. The given fan is obtained by the star subdivision of the first maximal cone throughBy the toric blowup at a torus-fixed point, this subdivision blows up the torus-fixed point corresponding to $\mathrm{Cone}(e_1,e_2)$. Hencefor that torus-fixed point $p$.