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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2312.12129 |
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| _version_ | 1866909479025508352 |
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| 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 |