Journal of the
Korean Mathematical Society JKMS

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.

Keywords: Fano variety, cylinders

MSC numbers: 14J45, 14E08, 14R05

Supported by: N. T. A. Hang was partially supported by Grant number ICRTM02_2021.04, awarded in the internal grant competition of the International Center for Research and Postgraduate Training in Mathematics, Hanoi and IMU Breakout Graduate Fellowship (IMU-BGF-2021-03). M. Hoff was partially supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 286237555 - TRR 195. H. L. Truong was partially supported by the Alexander von Humboldt Foundation and the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2019.309.