A four-dimensional cousin of the Segre cubic

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-20 DOI:10.4171/rmi/1448

Laurent Manivel

引用次数: 1

Abstract

This note is devoted to a special Fano fourfold defined by a four-dimensional space of skew-symmetric forms in five variables. This fourfold appears to be closely related with the classical Segre cubic and its Cremona–Richmond configuration of planes. Among other exceptional properties, it is infinitesimally rigid and has Picard number six. We show how to construct it by blow-up and contraction, starting from a configuration of five planes in a four-dimensional quadric, compatibly with the symmetry group ${\mathcal S}\_5$. From this construction, we are able to describe the Chow ring explicitly.

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Segre立方的四维表亲

本文讨论由五变量的偏对称四维空间所定义的一种特殊的法诺四重。这种四重结构似乎与经典的塞格里立方及其克雷莫纳-里士满平面构型密切相关。在其他特殊性质中，它是无穷小刚性的并且有皮卡德数6。我们展示了如何从一个四维二次曲面上的五个平面的构型出发，通过放大和收缩来构造它，并与对称群${\mathcal S}\_5$相容。从这个结构中，我们可以明确地描述周氏环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.