Examples of cylindrical Fano fourfolds
Tóm tắt
We construct four different families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of the form
$$Z\,{\times }\,{\mathbb {A}}^{1}$$
, where Z is a quasiprojective variety. The affine cones over such a fourfold admit effective
$${\mathbb {G}}_{{\text {a}}}$$
-actions. Similar constructions of cylindrical Fano threefolds were done previously in the papers by Kishimoto et al. (Affine Algebraic Geometry. CRM Proceedings & Lecture Notes, vol 54, pp 123–163, 2011; Osaka J Math 51(4):1093–1112, 2014).
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