Equi-affine minimal-degree moving frames for polynomial curves
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914866843877376 |
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| author | Hong, Hoon Kogan, Irina A. |
| author_facet | Hong, Hoon Kogan, Irina A. |
| contents | We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-preserving affine transformations of the ambient space and the parameter shifts. We show that any matrix-completion algorithm can be turned into an equivariant moving frame algorithm via an equivariantization procedure that we develop. We prove that if a matrix-completion algorithm is of minimal degree then so is the resulting equivariant moving frame algorithm. We propose a novel minimal-degree matrix-completion algorithm, complementing the existing body of literature on this topic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06610 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equi-affine minimal-degree moving frames for polynomial curves Hong, Hoon Kogan, Irina A. Algebraic Geometry 14Q05, 14L24, 68W30 I.1.2 We develop a theory and an algorithm for constructing minimal-degree polynomial moving frames for polynomial curves in an affine space. The algorithm is equivariant under volume-preserving affine transformations of the ambient space and the parameter shifts. We show that any matrix-completion algorithm can be turned into an equivariant moving frame algorithm via an equivariantization procedure that we develop. We prove that if a matrix-completion algorithm is of minimal degree then so is the resulting equivariant moving frame algorithm. We propose a novel minimal-degree matrix-completion algorithm, complementing the existing body of literature on this topic. |
| title | Equi-affine minimal-degree moving frames for polynomial curves |
| topic | Algebraic Geometry 14Q05, 14L24, 68W30 I.1.2 |
| url | https://arxiv.org/abs/2402.06610 |