The $F$-adjoined Gauss Map and Gaussian Likelihood Geometry
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912150171156480 |
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| author | Gustafsson, Lukas |
| author_facet | Gustafsson, Lukas |
| contents | We introduce the F-adjoined Gauss map. We use it to express the Gaussian maximum likelihood degree as a product of two invariants. As an application of our product formula, we classify all projective curves of Gaussian maximum likelihood degree 1. We also provide a formula for the generic Gaussian maximum likelihood degree of a projective variety $X$ in terms of its polar classes. The renowned polar class formula for generic Euclidean distance degree is a special case of our formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03503 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The $F$-adjoined Gauss Map and Gaussian Likelihood Geometry Gustafsson, Lukas Algebraic Geometry 62R01, 14E05, 35C11, 35F20 We introduce the F-adjoined Gauss map. We use it to express the Gaussian maximum likelihood degree as a product of two invariants. As an application of our product formula, we classify all projective curves of Gaussian maximum likelihood degree 1. We also provide a formula for the generic Gaussian maximum likelihood degree of a projective variety $X$ in terms of its polar classes. The renowned polar class formula for generic Euclidean distance degree is a special case of our formula. |
| title | The $F$-adjoined Gauss Map and Gaussian Likelihood Geometry |
| topic | Algebraic Geometry 62R01, 14E05, 35C11, 35F20 |
| url | https://arxiv.org/abs/2311.03503 |