The variety of orthogonal frames
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908741815762944 |
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| author | Casabella, Laura Sammartano, Alessio |
| author_facet | Casabella, Laura Sammartano, Alessio |
| contents | An orthogonal n-frame is an ordered set of n pairwise orthogonal vectors. The set of all orthogonal n-frames in a d-dimensional quadratic vector space is an algebraic variety V(d,n). In this paper, we investigate the variety V(d,n) as well as the quadratic ideal I(d,n) generated by the orthogonality relations, which cuts out V(d,n). We classify the irreducible components of V(d,n), give criteria for the ideal I(d,n) to be prime or a complete intersection, and for the variety V(d,n) to be normal. We also give near-equivalent conditions for V(d,n) to be factorial. Applications are given to the theory of Lovász-Saks-Schrijver ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_25058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The variety of orthogonal frames Casabella, Laura Sammartano, Alessio Commutative Algebra Algebraic Geometry Primary: 13F70, Secondary: 05C62, 05E40, 13A50, 13B22, 13C40, 13F15, 13H10, 14C05, 14L30, 14M17, 15A63 An orthogonal n-frame is an ordered set of n pairwise orthogonal vectors. The set of all orthogonal n-frames in a d-dimensional quadratic vector space is an algebraic variety V(d,n). In this paper, we investigate the variety V(d,n) as well as the quadratic ideal I(d,n) generated by the orthogonality relations, which cuts out V(d,n). We classify the irreducible components of V(d,n), give criteria for the ideal I(d,n) to be prime or a complete intersection, and for the variety V(d,n) to be normal. We also give near-equivalent conditions for V(d,n) to be factorial. Applications are given to the theory of Lovász-Saks-Schrijver ideals. |
| title | The variety of orthogonal frames |
| topic | Commutative Algebra Algebraic Geometry Primary: 13F70, Secondary: 05C62, 05E40, 13A50, 13B22, 13C40, 13F15, 13H10, 14C05, 14L30, 14M17, 15A63 |
| url | https://arxiv.org/abs/2512.25058 |