Projective self-dual polygons in higher dimensions

Abstract

Abstract This paper examines the moduli space M m ,n,k of m-self-dual n-gons in ℙ k . We present an explicit construction of self-dual polygons and determine the dimension of M m ,n,k for certain n and m. Additionally, we propose a conjecture that extends Clebsch’s theorem, which states that every pentagon in ℝℙ2 is invariant under the Pentagram map.