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

Solution

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

 Solution

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