Waring decompositions of special binomials
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909964630491136 |
|---|---|
| author | Chiantini, Luca Gesmundo, Fulvio Marziali, Sara |
| author_facet | Chiantini, Luca Gesmundo, Fulvio Marziali, Sara |
| contents | We determine the Waring rank of homogeneous polynomials of the form $x^ky^kz^k + \ell^{3k}$ where $\ell$ is a linear form. The result is based on the study of the Hilbert function and the resolution of special configurations of points in $\mathbb{P}^2$. As a byproduct of our result, we show that the monomial $x^ky^kz^k$ does not have irredundant decompositions of length $(k+1)^2 +1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Waring decompositions of special binomials Chiantini, Luca Gesmundo, Fulvio Marziali, Sara Algebraic Geometry 14N07, 14N05, 15A69 We determine the Waring rank of homogeneous polynomials of the form $x^ky^kz^k + \ell^{3k}$ where $\ell$ is a linear form. The result is based on the study of the Hilbert function and the resolution of special configurations of points in $\mathbb{P}^2$. As a byproduct of our result, we show that the monomial $x^ky^kz^k$ does not have irredundant decompositions of length $(k+1)^2 +1$. |
| title | Waring decompositions of special binomials |
| topic | Algebraic Geometry 14N07, 14N05, 15A69 |
| url | https://arxiv.org/abs/2512.13805 |