## Osaka Journal of Mathematics

### Affine cones over Fano threefolds and additive group actions

#### Abstract

In this paper we address the following questions for smooth Fano threefolds of Picard number 1: \begin{itemize} \item \textit{When does such a threefold $X$ possess an open cylinder $U \simeq Z\times\mathbb{A}^{1}$, where $Z$ is a surface?} \item \textit{When does an affine cone over $X$ admit an effective action of the additive group of the base field?} \end{itemize} A geometric criterion from [26] (see also [27]) says that the two questions above are equivalent. In [26] we found some interesting families of Fano threefolds carrying a cylinder. Here we provide new such examples.

#### Article information

Source
Osaka J. Math., Volume 51, Number 4 (2014), 1093-1113.

Dates
First available in Project Euclid: 31 October 2014

https://projecteuclid.org/euclid.ojm/1414761913

Mathematical Reviews number (MathSciNet)
MR3273879

Zentralblatt MATH identifier
1308.14066

#### Citation

Kishimoto, Takashi; Prokhorov, Yuri; Zaidenberg, Mikhail. Affine cones over Fano threefolds and additive group actions. Osaka J. Math. 51 (2014), no. 4, 1093--1113. https://projecteuclid.org/euclid.ojm/1414761913

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