Rationality conjecture for simply connected quotient surfaces

Let $S$ be a projective surface with quotient singularities such that

$$H^2(S,\mathbb{Q})\cong\mathbb{Q}$$

and let $S^0$ denote its smooth locus. Assume that $S^0$ is simply connected. Rationality conjecture. Then $S$ is rational.

The author presents this as a precise form of a suggested general phenomenon concerning simply connected surfaces with $q=p_g=0$ and small Picard number. It is needed for the classification of Seifert structures on simply connected rational homology spheres; no resolution is supplied here.