On cylindrical smooth rational Fano fourfolds
Abstract
We construct new families of smooth Fano fourfolds with Picard rank 1 which contain open A1-cylinders, that is, Zariski open subsets of the form Z × A1, where Z is a quasiprojective variety. In particular, we show that every Mukai fourfold of genus 8 is cylindrical and there exists a family of cylindrical Gushel-Mukai fourfolds.
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