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Article Dans Une Revue Revista Matemática Iberoamericana Année : 2024

A four-dimensional cousin of the Segre cubic

Résumé

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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Dates et versions

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

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Laurent Manivel. A four-dimensional cousin of the Segre cubic. Revista Matemática Iberoamericana, 2024, 40 (3), pp.1089-1114. ⟨10.4171/RMI/1448⟩. ⟨hal-03871778⟩
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