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A four-dimensional cousin of the Segre cubic

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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 explicitely.
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hal-03871778 , version 1 (25-11-2022)

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Laurent Manivel. A four-dimensional cousin of the Segre cubic. 2022. ⟨hal-03871778⟩
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