Let $X$ be a log del Pezzo surface of rank one. In , the first author determined the possible singularity type of $X$ when $X$ contains the affine plane as a Zariski open subset. In this paper, we prove that, if $X$ contains a non-cyclic quotient singular point and its singularity type is one of the list of [8, Appendix C], then it contains the affine plane as a Zariski open subset.
This work was supported by JSPS KAKENHI Grant Numbers JP16K05094, JP17K05198.
"Log del Pezzo surfaces of rank one containing the affine plane." Nihonkai Math. J. 29 (2) 77 - 130, 2018.