Irrationality of the general smooth quartic $3$-fold using intermediate Jacobians
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916634569998336 |
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| author | Farb, Benson |
| author_facet | Farb, Benson |
| contents | We prove that the intermediate Jacobian of the Klein quartic $3$-fold $X$ is not isomorphic, as a principally polarized abelian variety, to a product of Jacobians of curves. As corollaries we deduce (using a criterion of Clemens-Griffiths) that $X$, as well as the general smooth quartic $3$-fold, is irrational. These corollaries were known: Iskovskih-Manin \cite{IM} proved that every smooth quartic $3$-fold is irrational. However, the method of proof here is different than that of \cite{IM} and is significantly simpler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Irrationality of the general smooth quartic $3$-fold using intermediate Jacobians Farb, Benson Algebraic Geometry We prove that the intermediate Jacobian of the Klein quartic $3$-fold $X$ is not isomorphic, as a principally polarized abelian variety, to a product of Jacobians of curves. As corollaries we deduce (using a criterion of Clemens-Griffiths) that $X$, as well as the general smooth quartic $3$-fold, is irrational. These corollaries were known: Iskovskih-Manin \cite{IM} proved that every smooth quartic $3$-fold is irrational. However, the method of proof here is different than that of \cite{IM} and is significantly simpler. |
| title | Irrationality of the general smooth quartic $3$-fold using intermediate Jacobians |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.16084 |