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arXiv · 1106.1312

Affine cones over Fano threefolds and additive group actions

Takashi Kishimoto·Yuri Prokhorov·Mikhail Zaidenberg
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Abstract

We address the following question: When an affine cone over a smooth Fano threefold admits an effective action of the additive group? In this paper we deal with Fano threefolds of index 1 and Picard number 1. Our approach is based on a geometric criterion from our previous paper, which relates the existence of an additive group action on the cone over a smooth projective variety X with the existence of an open polar cylinder in X. Non-trivial families of Fano threefolds carrying a cylinder were found in loc. cit. Here we provide new such examples.

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Takashi Kishimoto, Yuri Prokhorov, Mikhail Zaidenberg. 2011-06-07. Affine cones over Fano threefolds and additive group actions. https://arxiv.org/abs/1106.1312

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