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arXiv · 2606.18387

A Pascal-type construction of the Segre cubic and the Cremona--Richmond configuration

Piotr Pokora·Tomasz Szemberg
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Abstract

We present a Pascal-type residual construction in P^4. Starting from two quadruples of hyperplanes whose four diagonal intersection planes lie in a hyperplane, we show that the twelve residual planes lie on a cubic threefold. In the general case this cubic is the Segre cubic, and the construction recovers its fifteen planes and the associated Cremona--Richmond configuration. We also exhibit a point-line realization of this configuration in P^4 and show that it gives a (5,3)-geprofi set.

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Piotr Pokora, Tomasz Szemberg. 2026-06-16. A Pascal-type construction of the Segre cubic and the Cremona--Richmond configuration. https://arxiv.org/abs/2606.18387

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