Manin and Schechtman introduced Discriminantal arrangement as generalizing classical braid arrangement. We show that the points in specific degree 2 hypersurface in Grassmannian correspond to generic arrangements of n hyperplanes in 3-dimensional space with associated discriminantal arrangement having intersections of multiplicity 3 in codimension two. In particular each component of this hypersurface is intersection of Grassmannian with a quadric.

The purpose of this short talk is to restate Pappus's theorem in terms of quadrics. Moreover I will classify the intersections of quadrics with arrangement in Hesse configuration in complex case.

This talk is based on a joint work with S. Settepanella and S. Yamagata.