Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 152 / 2 / a / i / Solution

For the rays $v_1=(1,0)$, $v_2=(0,1)$, and $v_3=(-a,-b)$, the determinants of consecutive pairs have absolute valuesBy the smoothness criterion for a toric variety, $\mathbb{P}(1,a,b)$ is smooth exactly when $a=b=1$.