A rationality criterion for projective surfaces - partial solution to Kollar's conjecture

Abstract

Kollár's conjecture states that a complex projective surface $S$ with quotient singularities and with $H^2(S,\mathbb{Q})\cong \mathbb{Q}$ should be rational if its smooth part $S^0$ is simply connected. We confirm the conjecture under the additional condition that the exceptional divisor in a minimal resolution of $S$ has at most 3 components over each singular point of $S$.

An error in the previous version was corrected. To appear in the Proceedings of the Conference in honor of Igor Dolgachev on his 60th birthday