Projective-geometric correspondence conjecture for WDVV systems

A WDVV system is a system of first-order PDEs considered together with its projective-geometric structures. A quadratic line complex is the associated family of lines in projective space defined by a quadratic condition, and a linear line congruence is a family of lines defined linearly in the relevant Plücker coordinates. Projective-geometric correspondence conjecture. To every WDVV system there are associated a quadratic line complex and a linear line congruence. In the known cases, projective reciprocal transformations exhibit these structures and make the bi-Hamiltonian WDVV hierarchy a projective-geometric object; their existence for every WDVV system remains open.