Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)

We show that points in specific degree-2 hypersurfaces in the Grassmannian G r ( 3 , n ) correspond to generic arrangements of n hyperplanes in C 3 with associated discriminantal arrangement having intersections of multiplicity three in codimension two.