A four-dimensional cousin of the Segre cubic

Laurent Manivel (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Géométrie algébrique [math.AG]

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