Ovoids of $Q^+(7,q)$ of low-degree
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_ | 1866912219154874368 |
|---|---|
| author | Bartoli, Daniele Durante, Nicola Grimaldi, Giovanni Giuseppe Timpanella, Marco |
| author_facet | Bartoli, Daniele Durante, Nicola Grimaldi, Giovanni Giuseppe Timpanella, Marco |
| contents | Ovoids of the hyperbolic quadric $Q^+(7,q)$ of $\mathrm{PG}(7,q)$ have been extensively studied over the past 40 years, partly due to their connections with other combinatorial objects. It is well known that the points of an ovoid of $Q^+(7,q)$ can be parametrized by three polynomials $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$. In this paper, we classify ovoids of $Q^+(7,q)$ of low degree, specifically under the assumption that $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$ have degree at most 3. Our approach relies on the analysis of an algebraic hypersurface associated with the ovoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02219 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ovoids of $Q^+(7,q)$ of low-degree Bartoli, Daniele Durante, Nicola Grimaldi, Giovanni Giuseppe Timpanella, Marco Combinatorics Algebraic Geometry 05B25, 11T06, 51E20 Ovoids of the hyperbolic quadric $Q^+(7,q)$ of $\mathrm{PG}(7,q)$ have been extensively studied over the past 40 years, partly due to their connections with other combinatorial objects. It is well known that the points of an ovoid of $Q^+(7,q)$ can be parametrized by three polynomials $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$. In this paper, we classify ovoids of $Q^+(7,q)$ of low degree, specifically under the assumption that $f_1(X,Y,Z)$, $f_2(X,Y,Z)$, $f_3(X,Y,Z)$ have degree at most 3. Our approach relies on the analysis of an algebraic hypersurface associated with the ovoid. |
| title | Ovoids of $Q^+(7,q)$ of low-degree |
| topic | Combinatorics Algebraic Geometry 05B25, 11T06, 51E20 |
| url | https://arxiv.org/abs/2502.02219 |