On cylindrical smooth rational Fano fourfolds
J. Korean Math. Soc. 2022 Vol. 59, No. 1, 87-103
https://doi.org/10.4134/JKMS.j210140
Published online November 8, 2021
Printed January 1, 2022
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 : 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.
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd