Projective self-dual polygons in higher dimensions
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Ana Chavez-Caliz
Abstract
This paper examines the moduli space Mm,n,k of m-self-dual n-gons in ℙk. We present an explicit construction of self-dual polygons and determine the dimension of Mm,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.
Funding statement: This research was supported by the U.S. National Science Foundation through the grant DMS-2005444 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 281071066 – TRR 191.
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Communicated by: S. Weintraub
Acknowledgements
The author would like to thank Sergei Tabachnikov, Gil Bor, Boris Khesin and Richard Schwartz for their insightful discussions and valuable feedback. Additionally, many thanks to Jack Huizenga for sharing the paper by Horn and Sergeichuk [10], which was crucial for understanding the bilinear forms associated with dual polygons. I would like to express my sincere gratitude to the reviewer for their valuable feedback and suggestions.
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Articles in the same Issue
- Frontmatter
- Exploring tropical differential equations
- On the bond polytope
- Universal convex covering problems under translations and discrete rotations
- Ehrhart theory of paving and panhandle matroids
- A partial compactification of the Bridgeland stability manifold
- The geometry of discrete L-algebras
- Projective self-dual polygons in higher dimensions
Articles in the same Issue
- Frontmatter
- Exploring tropical differential equations
- On the bond polytope
- Universal convex covering problems under translations and discrete rotations
- Ehrhart theory of paving and panhandle matroids
- A partial compactification of the Bridgeland stability manifold
- The geometry of discrete L-algebras
- Projective self-dual polygons in higher dimensions
