Projective Self-dual polygons in higher dimensions

Chavez-Caliz; Ana C

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arXiv · 2112.00177

Projective Self-dual polygons in higher dimensions

Chavez-Caliz·Ana C

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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 \mathbb{RP}^2 is invariant under the Pentagram map.

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Chavez-Caliz, Ana C. 2021-11-30. Projective Self-dual polygons in higher dimensions. https://arxiv.org/abs/2112.00177

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