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October 2014 Affine cones over Fano threefolds and additive group actions
Takashi Kishimoto, Yuri Prokhorov, Mikhail Zaidenberg
Osaka J. Math. 51(4): 1093-1113 (October 2014).

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.

Citation

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Takashi Kishimoto. Yuri Prokhorov. Mikhail Zaidenberg. "Affine cones over Fano threefolds and additive group actions." Osaka J. Math. 51 (4) 1093 - 1113, October 2014.

Information

Published: October 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1308.14066
MathSciNet: MR3273879

Subjects:
Primary: 14J45, 14R20
Secondary: 14J50, 14R05

Rights: Copyright © 2014 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
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Vol.51 • No. 4 • October 2014
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