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Geproci sets in P3 in linear general position beyond four points

Determine whether any geproci set of points exists in P3 in linear general position other than a set of four general points; equivalently, resolve the conjecture that no geproci sets in P3 in linear general position exist apart from four general points.

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Background

The paper contrasts geprofi sets in P4 with geproci sets in P3. It recalls a conjecture from the literature stating that geproci sets in P3 in LGP should not exist beyond four points, and notes that this question remains unresolved.

This longstanding open problem frames the LGP landscape in P3 and provides context for the abundance of geprofi examples in P4 studied in this work.

References

In [4] the authors conjectured that geproci sets in P3 in linear general position (henceforth denoted LGP) do not exist apart from 4 general points. This question is still open.

— Finite sets of points in $\mathbb{P}^4$ with special projection properties (2407.01744 - Chiantini et al., 1 Jul 2024) in Section 1 (Introduction)