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

Sumire Sawada, Simona Settepanella, So Yamagata

Abstract


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.


Keywords


Discriminantal arrangements, intersection lattice, Grassmannian, Pappus's Theorem

Full Text:

PDF


DOI: https://doi.org/10.26493/1855-3974.1619.a03

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications