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arXiv · 2211.16154

A four-dimensional cousin of the Segre cubic

Laurent Manivel
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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 $S_5$. From this construction we are able to describe the Chow ring explicitly.

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Laurent Manivel. 2022-11-29. A four-dimensional cousin of the Segre cubic. https://arxiv.org/abs/2211.16154

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