We prove that a log del Pezzo surface of Picard number one contains at most $3$ singular points if its smooth locus is simply connected. This establishes the algebraic Montgomery-Yang problem for log del Pezzo surfaces.
"Algebraic Montgomery-Yang problem: the log del Pezzo surface case." J. Math. Soc. Japan 66 (4) 1073 - 1089, October, 2014. https://doi.org/10.2969/jmsj/06641073