Let S be a del Pezzo surface with at worst Du Val singularities such that it is a hypersurface in a weighted projective space ℙ. We prove that the surface S contains a (−K_S)-polar cylinder if and only if the automorphism group of the affine variety ℙ \ S contains a unipotent subgroup.

中文翻译：

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G a $$ {\ mathbbm {G}} _ a $$-超曲面补缀上的操作

令S为Du Val奇异度最差的del Pezzo曲面，使得它是加权投影空间ℙ中的超曲面。我们证明，当且仅当仿射变种ℙ\ S的自同构群包含一个单能子群时，表面S包含一个（-K _S）极圆柱。