Projective Self-dual polygons in higher dimensions

2021/11/30 by Ana Chen, Chavez-Caliz, C, Ana
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2112.00177

openalex publication_date 2021/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Motivated by a question from V. Arnold about self-dual curves in projective spaces, we study \cal M_m,n,k: the moduli space of m-self-dual n-gons in \mathbb P^k. This paper lays out an explicit construction of self-dual polygons, and for specific cases of n and m, provides the dimension of \cal M_m,n,k. We include a conjecture about the Pentagram map in higher dimensions that generalizes Clebsch's theorem, which states that every pentagon in \mathbbRP² is invariant under the Pentagram map.

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