## Advanced Studies in Pure Mathematics

### New examples of cylindrical Fano fourfolds

#### Abstract

We produce new families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of form $Z\times{\mathbb A}^1$, where $Z$ is a quasiprojective variety. The affine cones over such a fourfold admit effective $\mathbb{G}_{\operatorname{a}}$-actions. Similar constructions of cylindrical Fano threefolds and fourfolds were done previously in [KPZ11, KPZ14, PZ16].

#### Article information

Dates
Revised: 12 February 2016
First available in Project Euclid: 21 September 2018

https://projecteuclid.org/ euclid.aspm/1537498715

Digital Object Identifier
doi:10.2969/aspm/07510443

Mathematical Reviews number (MathSciNet)
MR3793372

Zentralblatt MATH identifier
1396.14062

#### Citation

Prokhorov, Yuri; Zaidenberg, Mikhail. New examples of cylindrical Fano fourfolds. Algebraic Varieties and Automorphism Groups, 443--463, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510443. https://projecteuclid.org/euclid.aspm/1537498715