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arXiv · 1212.4479

Unipotent Group Actions on Del Pezzo Cones

Takashi Kishimoto·Yuri Prokhorov·Mikhail Zaidenberg
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Abstract

In a previous paper we established that for any del Pezzo surface Y of degree at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear system admits an effective Ga-action. In particular, the group Aut(X) is infinite dimensional. In contrast, we show in this note that for a del Pezzo surface Y of degree at most 2 the generalized cones X as above do not admit any non-trivial action of a unipotent algebraic group.

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Takashi Kishimoto, Yuri Prokhorov, Mikhail Zaidenberg. 2012-12-18. Unipotent Group Actions on Del Pezzo Cones. https://arxiv.org/abs/1212.4479

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