The Stack of Similarity Classes of Triangles
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866918107903164416 |
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| author | Brussel, Eric Goertz, Madeleine Guptill, Elijah Lyle, Kelly |
| author_facet | Brussel, Eric Goertz, Madeleine Guptill, Elijah Lyle, Kelly |
| contents | We construct the smooth, compact moduli space of similarity classes of labeled, oriented triangles. The space, denoted $\mathfrak D$, is a connected sum of three projective planes, and projects via blowdown to two shape spaces that have appeared in the literature: the well-known (Riemann) sphere (\cite{Kend84}, \cite{Beh}, \cite{Montgomery}, \cite{ES15}), and the less-well-known 2-torus (\cite{BG23}). A natural action by the dihedral group $D_6$ defines the quotient stack $[\mathfrak D/D_6]$ of absolute (unlabeled, unoriented) classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Stack of Similarity Classes of Triangles Brussel, Eric Goertz, Madeleine Guptill, Elijah Lyle, Kelly Algebraic Geometry Dynamical Systems 14D23 (Primary) 15M05, 70F99 (Secondary) We construct the smooth, compact moduli space of similarity classes of labeled, oriented triangles. The space, denoted $\mathfrak D$, is a connected sum of three projective planes, and projects via blowdown to two shape spaces that have appeared in the literature: the well-known (Riemann) sphere (\cite{Kend84}, \cite{Beh}, \cite{Montgomery}, \cite{ES15}), and the less-well-known 2-torus (\cite{BG23}). A natural action by the dihedral group $D_6$ defines the quotient stack $[\mathfrak D/D_6]$ of absolute (unlabeled, unoriented) classes. |
| title | The Stack of Similarity Classes of Triangles |
| topic | Algebraic Geometry Dynamical Systems 14D23 (Primary) 15M05, 70F99 (Secondary) |
| url | https://arxiv.org/abs/2408.07792 |