Algebraic criterion for projective infinitesimal flexibility

Determine whether an algebraic condition characterizes projective infinitesimal flexibility for an incidence geometry that has isostatic realizations, using tie-downs formed by the admissible projective pinning systems.

Background

The projective rigidity matrix is square after suitable pinning of four points, four lines, three points and a line, or three lines and a point. The unresolved question is whether the determinant or related polynomial data yield a projectively invariant criterion for special flexible or self-stressed realizations.

References

In the setting of projective rigidity, we can again ask if there is an algebraic condition for projective infinitesimal flexibility of an incidence geometry that has isostatic realizations.

— 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"