Examples of cylindrical Fano fourfolds
Yuri Prokhorov, Mikhail Zaidenberg (IF)
TL;DR
This paper constructs four new families of smooth Fano fourfolds with Picard rank 1 that contain cylinders, and shows their affine cones admit effective Ga-actions, extending previous work on Fano threefolds.
Contribution
It introduces four new families of cylindrical Fano fourfolds with Picard rank 1, expanding the known examples and properties of such varieties.
Findings
Constructed four families of cylindrical Fano fourfolds
Affine cones over these fourfolds admit effective Ga-actions
Extended previous constructions from Fano threefolds to fourfolds
Abstract
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Mathematical Dynamics and Fractals · Advanced Combinatorial Mathematics