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http://dx.doi.org/10.4134/JKMS.j210140

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)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.1, 2022 , pp. 87-103 More about this Journal
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
Fano variety; cylinders;
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