Chasles's ten-point quadric problem

Determine geometric conditions under which ten given points in three-dimensional projective space lie on a quadric surface.

Background

The paper cites Chasles's classical question concerning ten points and quadric surfaces in three-dimensional space. It explicitly states that this problem remains unresolved, while noting that collinear triples can create projective constructions.

References

Michel Chasles asked, about 200 years ago, for geometric conditions under which 10 given points lie on a quadric surface in 3-space, and this question is still unanswered.

— Counting for rigidity under projective transformations in the plane  (2503.07228 - Berman et al., 10 Mar 2025) in Section "Open problems and future work," subsection "Extensions to higher dimensions"