An arithmetic count of osculating lines
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909479025508352 |
|---|---|
| author | Muratore, Giosuè |
| author_facet | Muratore, Giosuè |
| contents | We say that a line in $\mathbb P^{n+1}_k$ is osculating to a hypersurface $Y$ if they meet with contact order $n+1$. When $k=\mathbb C$, it is known that through a fixed point of $Y$, there are exactly $n!$ of such lines. Under some parity condition on $n$ and $\mathrm{deg}(Y)$, we define a quadratically enriched count of these lines over any perfect field $k$. The count takes values in the Grothendieck--Witt ring of quadratic forms over $k$ and depends linearly on $\mathrm{deg}(Y)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12129 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An arithmetic count of osculating lines Muratore, Giosuè Algebraic Geometry 14N15, 11E81, 14F42 We say that a line in $\mathbb P^{n+1}_k$ is osculating to a hypersurface $Y$ if they meet with contact order $n+1$. When $k=\mathbb C$, it is known that through a fixed point of $Y$, there are exactly $n!$ of such lines. Under some parity condition on $n$ and $\mathrm{deg}(Y)$, we define a quadratically enriched count of these lines over any perfect field $k$. The count takes values in the Grothendieck--Witt ring of quadratic forms over $k$ and depends linearly on $\mathrm{deg}(Y)$. |
| title | An arithmetic count of osculating lines |
| topic | Algebraic Geometry 14N15, 11E81, 14F42 |
| url | https://arxiv.org/abs/2312.12129 |