Examples of cylindrical Fano fourfolds

Yuri Prokhorov (1) , Mikhail Zaidenberg (2)

1 SMI | RAS - Steklov Mathematical Institute [Moscow]
2 IF - Institut Fourier

We construct 4 di erent families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of the form Z x A1, where Z is a quasiprojective variety. The affi ne cones over such a fourfold admit eff ective Ga-actions. Similar constructions of cylindrical Fano threefolds were done previously in our papers jointly with Takashi Kishimoto.

Mots clés: automorphism; group action of the additive group; Fano variety; Affine cone

Domaines: Géométrie algébrique [math.AG]

Yuri Prokhorov, Mikhail Zaidenberg. Examples of cylindrical Fano fourfolds. European Journal of Mathematics, 2016, 2 (1), pp.262-282. ⟨10.1007/s40879-015-0051-7⟩. ⟨hal-01007615⟩