Pappus's Theorem in Grassmannian Gr (3, ℂⁿ)

In this paper we study intersections of quadrics, components of the hypersurface in the Grassmannian Gr(3, ℂn) introduced by S. Sawada, S. Settepanella and S. Yamagata in 2017. This lead to an alternative statement and proof of Pappus’s Theorem retrieving Pappus’s and Hesse configurations of lines as special points in the complex projective Grassmannian. This new connection is obtained through a third purely combinatorial object, the intersection lattice of Discriminantal arrangement.