6 problems

Hereditary freeness conjecture. For any vee-system $\mathcal A$, the associated arrangement $\Delta_{\mathcal A}$ is hereditarily free.

Feigin–Veselov factorization conjecture. All arrangements of vee-systems are free, so the corresponding Poincare polynomials are always factorizable in such a form.

Feigin–Veselov freeness conjecture. The hyperplane arrangement of any vee-system is free in Saito's sense.

Extension conjecture. The values of the $\nu$-functions on the corresponding flats of an irreducible $\vee$-system and its extension are proportional.

Uniqueness conjecture. An irreducible $\vee$-system $\mathcal{A}$ is uniquely determined, modulo the linear group $GL(V^*)$, by its matroid $M$ and the corresponding $\nu$-function…

Harmonic-bundle conjecture. The corresponding four lines form a harmonic bundle with two orthogonals.