Rational lines on cubic hypersurfaces II
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917097259401216 |
|---|---|
| author | Brandes, Julia Dietmann, Rainer Leep, David B. |
| author_facet | Brandes, Julia Dietmann, Rainer Leep, David B. |
| contents | We show that any rational cubic hypersurface of dimension at least 33 defined over a number field $K$ vanishes on a $K$-rational projective line, reducing the previous lower bound of Wooley by two. For $K=\mathbb Q$ we can reduce the bound to 29. The main ingredients are a result on linear spaces on quadratic forms over suitable non-real quadratic field extensions, and recent work of Bernert and Hochfilzer on cubic forms over imaginary quadratic number fields for the rational case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09449 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational lines on cubic hypersurfaces II Brandes, Julia Dietmann, Rainer Leep, David B. Number Theory Primary: 11D72. Secondary: 11E76, 14G05, 14J70 We show that any rational cubic hypersurface of dimension at least 33 defined over a number field $K$ vanishes on a $K$-rational projective line, reducing the previous lower bound of Wooley by two. For $K=\mathbb Q$ we can reduce the bound to 29. The main ingredients are a result on linear spaces on quadratic forms over suitable non-real quadratic field extensions, and recent work of Bernert and Hochfilzer on cubic forms over imaginary quadratic number fields for the rational case. |
| title | Rational lines on cubic hypersurfaces II |
| topic | Number Theory Primary: 11D72. Secondary: 11E76, 14G05, 14J70 |
| url | https://arxiv.org/abs/2307.09449 |