Solution
= Solution
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 $a=b=1$.