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On cylindrical smooth rational Fano fourfolds (2101.04441v2)
Published 12 Jan 2021 in math.AG
Abstract: We construct new families of smooth Fano fourfolds with Picard rank $1$ which contain open $\Bbb A1$-cylinders, that is, Zariski open subsets of the form $Z \times \Bbb A1$, 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.