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 $H^2(S,\bbQ)\cong \bbQ$ 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
.