## Log del Pezzo surfaces of rank one containing the affine plane.(English)Zbl 1419.14056

Summary: Let $$X$$ be a log del Pezzo surface of rank one. In [Nihonkai Math. J. 12, No. 2, 165–195; appendix A: 185–186; appendix B: 186–189; appendix C 189–193 (2001; Zbl 1031.14020)], 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 [loc. cit., Appendix C], then it contains the affine plane as a Zariski open subset.

### MSC:

 14J26 Rational and ruled surfaces 14J17 Singularities of surfaces or higher-dimensional varieties

Zbl 1031.14020
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### References:

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