Journal of the
Korean Mathematical Society

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



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

Online first article January 1, 2022      Printed January 1, 2022

Copyright © The Korean Mathematical Society.

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


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.

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