Generic projections of the $\mathrm{H}_{4}$ configuration of points

TL;DR

This paper presents an example of a finite point set in projective 3-space with the geproci property that is neither a grid nor a half-grid, addressing an open question in algebraic geometry.

Contribution

It provides the first known example of such a set, expanding understanding of geproci configurations beyond traditional grid structures.

Findings

Identifies a new class of geproci point sets in $ ext{P}^3$

Demonstrates the existence of non-grid, non-half-grid geproci sets

Answers an open question posed by Pokora, Szemberg, and Szpond

Abstract

In the present note we give an example of a finite set of points in $\mathbb{P}^{3}$ which has the so-called geproci property, but it is neither a grid nor a half-grid. This answers a question on the existence of such sets rised by Pokora, Szemberg and Szpond [arXiv:2010.08863].