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Статья

Affine cones over Fano threefolds and additive group actions

Osaka Journal of Mathematics. 2014. Vol. 51. No. 4. P. 1093-1113.
Kishimoto T., Yuri Prokhorov, Zaidenberg M.

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.