A four-dimensional cousin of the Segre cubic
Algebraic Geometry
2022-11-30 v1
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 . From this construction we are able to describe the Chow ring explicitly.
Cite
@article{arxiv.2211.16154,
title = {A four-dimensional cousin of the Segre cubic},
author = {Laurent Manivel},
journal= {arXiv preprint arXiv:2211.16154},
year = {2022}
}