Cylinders in del Pezzo fibrations

Abstract

We show that a del Pezzo fibration $\pi$ : V $\to$ W of degre d contains a vertical open cylinder, that is, an open subset whose intersection with the generic fiber of $\pi$ is isomorphic to $Z\times {\mathbb{A}}_K^1$ for some quasi-projective variety Z defined over the function field K of W , if and only if d $\ge$ 5 and $\pi$ : V $\to$ W admits a rational section. We also construct twisted cylinders in total spaces of threefold del Pezzo fibrations $\pi$ : V $\to$ P 1 of degree d $\le$ 4.

References in corpus (2)

• Affine cones over Fano threefolds and additive group actions
• New examples of cylindrical Fano fourfolds

Cited by in corpus (1)

• Deformations of ${\mathbb{A}}^1$-cylindrical varieties