The Noether--Lefschetz theorem in arbitrary characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866913540964614144 |
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| author | Ji, Lena |
| author_facet | Ji, Lena |
| contents | We show that if $X\subset\mathbb P^N_k$ is a normal variety of dimension $\geq 3$ and $H\subset\mathbb P^N_k$ a very general hypersurface of degree $d=4$ or $\geq 6$, then the restriction map $\mathrm{Cl}(X)\to\mathrm{Cl}(X\cap H)$ is an isomorphism up to torsion. If $\dim X\geq 4$, the result holds for $d\geq 2$. The proof uses the relative Jacobian of a curve fibration, together with a specialization argument, and the result holds over fields of arbitrary characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_12962 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Noether--Lefschetz theorem in arbitrary characteristic Ji, Lena Algebraic Geometry 14C20 (Primary), 14C22, 14K30 (Secondary) We show that if $X\subset\mathbb P^N_k$ is a normal variety of dimension $\geq 3$ and $H\subset\mathbb P^N_k$ a very general hypersurface of degree $d=4$ or $\geq 6$, then the restriction map $\mathrm{Cl}(X)\to\mathrm{Cl}(X\cap H)$ is an isomorphism up to torsion. If $\dim X\geq 4$, the result holds for $d\geq 2$. The proof uses the relative Jacobian of a curve fibration, together with a specialization argument, and the result holds over fields of arbitrary characteristic. |
| title | The Noether--Lefschetz theorem in arbitrary characteristic |
| topic | Algebraic Geometry 14C20 (Primary), 14C22, 14K30 (Secondary) |
| url | https://arxiv.org/abs/2107.12962 |