Kollár's algebraic Montgomery–Yang conjecture

Let $S$ be a rational homology projective plane with quotient singularities, and write

$$S^0:=S\setminus\operatorname{Sing}(S).$$

The smooth locus $S^0$ is assumed to be simply connected. Kollár's algebraic Montgomery–Yang conjecture. If $S^0$ is simply connected, then $S$ has at most three singular points. This problem concerns the maximal number of quotient singularities on a rational homology projective plane and is an algebraic analogue of the Montgomery–Yang problem for pseudo-free smooth circle actions on the $5$-sphere. The source states that the present paper completely resolves it.