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

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

2005-10-07

arxiv.org/abs/math/0510137v3

Mathematics

Algebraic Geometry

An error in the previous version was corrected. To appear in the Proceedings of the Conference in honor of Igor Dolgachev on h

Scientific paper

Koll\'ar's conjecture states that a complex projective surface $S$ with quotient singularities and with $H^2(S,\bbQ)\cong \bbQ$ 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 $S$.

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