On cylindrical smooth rational Fano fourfolds

Abstract

We construct new families of smooth Fano fourfolds with Picard rank $1$ which contain open ${\mathbb{A}}^1$-cylinders, that is, Zariski open subsets of the form $Z\times {\mathbb{A}}^1$, 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.

revised version, accepted in the Journal of the Korean Mathematical Society. arXiv admin note: text overlap with arXiv:1406.6339 by other authors