We classify all complex surfaces with quotient singularities that do not contain any smooth rational curves under the assumption that the canonical divisor of the surface is not pseudo-effective. As a corollary, we show that if is a log del Pezzo surface such that, for every closed point , there is a smooth curve (locally analytically) passing through , then contains at least one smooth rational curve.
"Smooth Rational Curves on Singular Rational Surfaces." Michigan Math. J. 67 (1) 83 - 98, March 2018. https://doi.org/10.1307/mmj/1508810820