Examples of cylindrical Fano fourfolds. (English) Zbl 1375.14206
A quasi-projective algebraic variety is called cylindrical if it contains a Zariski dense open subset of the form \(Z\times\mathbb{A}^{1}\) for some quasi-projective variety \(Z\). The existence of such cylinders in smooth projective varieties is intimately related to that of algebraic actions of the additive group \(\mathbb{G}_{a}\) on their affine cones. In the article under review, the authors describe the construction of families of cylindrical Fano fourfolds of Picard rank \(1\) via explicit Sarkisov links. These include smooth intersections of two quadrics in \(\mathbb{P}^{6}\), del Pezzo fourfolds of degree \(5\), and positive dimensional moduli of Mukai fourfolds of genus \(7\) and \(8\).
Reviewer: Adrien Dubouloz (Dijon)
MSC:
| 14R20 | Group actions on affine varieties |
| 14J45 | Fano varieties |
| 14J50 | Automorphisms of surfaces and higher-dimensional varieties |
| 14R05 | Classification of affine varieties |
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