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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.09204 |
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| _version_ | 1866917510437142528 |
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| author | Pratt, Elizabeth |
| author_facet | Pratt, Elizabeth |
| contents | The Segre determinant is a polynomial which encodes the condition for points to lie on a bilinear hypersurface in the product of projective spaces. We study Segre determinants and compute them in various coordinate systems. We show that the Segre determinant represents the Chow-Lam form of a generic torus orbit in the Grassmannian. These Chow-Lam forms were introduced as a generalization of Chow forms for projective varieties, and enjoy many similar properties. We also present applications to algebraic vision and to Chow quotients of Grassmannians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09204 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Segre Determinant Pratt, Elizabeth Algebraic Geometry 14M15 The Segre determinant is a polynomial which encodes the condition for points to lie on a bilinear hypersurface in the product of projective spaces. We study Segre determinants and compute them in various coordinate systems. We show that the Segre determinant represents the Chow-Lam form of a generic torus orbit in the Grassmannian. These Chow-Lam forms were introduced as a generalization of Chow forms for projective varieties, and enjoy many similar properties. We also present applications to algebraic vision and to Chow quotients of Grassmannians. |
| title | The Segre Determinant |
| topic | Algebraic Geometry 14M15 |
| url | https://arxiv.org/abs/2505.09204 |