New examples of cylindrical Fano fourfolds

Abstract

International audienceWe produce new families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of form Z × A 1 , where Z is a quasiprojective variety. The affine cones over such a fourfold admit effective G a-actions. Similar constructions of cylindrical Fano threefolds and fourfolds were done previously in [KPZ11, KPZ14, PZ15]