On nonnegative invariant quartics in type A
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910319452880896 |
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| author | Debus, Sebastian Goel, Charu Kuhlmann, Salma Riener, Cordian |
| author_facet | Debus, Sebastian Goel, Charu Kuhlmann, Salma Riener, Cordian |
| contents | The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification, we analyse $A_n$-invariant quartics. We prove that the cones of invariant sums of squares and nonnegative forms are equal if and only if the number of variables is at most 3 or odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On nonnegative invariant quartics in type A Debus, Sebastian Goel, Charu Kuhlmann, Salma Riener, Cordian Algebraic Geometry 11E76, 14P10, 20C30 The equivariant nonnegativity versus sums of squares question has been solved for any infinite series of essential reflection groups but type A. As a first step to a classification, we analyse $A_n$-invariant quartics. We prove that the cones of invariant sums of squares and nonnegative forms are equal if and only if the number of variables is at most 3 or odd. |
| title | On nonnegative invariant quartics in type A |
| topic | Algebraic Geometry 11E76, 14P10, 20C30 |
| url | https://arxiv.org/abs/2402.03722 |