Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2008
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| _version_ | 1866916443215364096 |
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| author | Hulek, Klaus Kloosterman, Remke |
| author_facet | Hulek, Klaus Kloosterman, Remke |
| contents | In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective 4-space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0806_2025 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces Hulek, Klaus Kloosterman, Remke Algebraic Geometry Algebraic Topology In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective 4-space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case. |
| title | Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/0806.2025 |