Pure conditions for projective incidence rigidity

Determine whether the pure-condition theory for infinitesimal flexibility and self-stress in isostatic bar-and-joint frameworks transfers to point-line incidence geometries and their projective rigidity matrices.

Background

For bar-and-joint frameworks, projectively invariant polynomials characterize special realizations where generic independence fails. The paper asks whether an analogous algebraic condition exists for point-line incidence geometries, particularly for configurations having isostatic realizations.

References

Does this transfer to the theory of points, lines and incidences and the associated projective rigidity matrix?

— 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 "The pure conditions"