Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON CYLINDRICAL SMOOTH RATIONAL FANO FOURFOLDS

  • Hang, Nguyen Thi Anh (Department of Mathematics Thai Nguyen University of Education Thai Nguyen Province) ;
  • Hoff, Michael (Mathematik und Informatik Universitat des Saarlandes) ;
  • Truong, Hoang Le (Mathematik und Informatik Universitat des Saarlandes and Institute of Mathematics VAST and Thang Long Institute of Mathematics and Applied Sciences)
  • Received : 2021.03.01
  • Accepted : 2021.09.24
  • Published : 2022.01.01
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Abstract

We construct new families of smooth Fano fourfolds with Picard rank 1 which contain open 𝔸1-cylinders, that is, Zariski open subsets of the form Z × 𝔸1, 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

Acknowledgement

The authors wish to thank Frank-Olaf Schreyer for his useful suggestions about the topics in this paper. We thank Mikhail Zaidenberg for valuable comments and suggestions on an earlier draft.

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