Affine cones over Fano threefolds and additive group actions

Details Affine cones over Fano threefolds and additive group actions Affine cones over Fano threefolds and additive group actions

2011-06-07

arxiv.org/abs/1106.1312v1

Mathematics

Algebraic Geometry

20p

Scientific paper

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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