On cylindrical smooth rational Fano fourfolds

Nguyen Thi Anh Hang; Michael Hoff; Hoang Le Truong

doi:10.4134/JKMS.j210140

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(1): 87-103

Published online January 1, 2022 https://doi.org/10.4134/JKMS.j210140

On cylindrical smooth rational Fano fourfolds

Nguyen Thi Anh Hang, Michael Hoff, Hoang Le Truong

Thai Nguyen University of Education; Campus E2 4; and Thang Long Institute of Mathematics and Applied Sciences

Abstract

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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.

Keywords: Fano variety, cylinders

MSC numbers: 14J45, 14E08, 14R05