A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908350836375552 |
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| author | Pichon-Pharabod, Eric |
| author_facet | Pichon-Pharabod, Eric |
| contents | We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic invariants of the surface, notably the Néron-Severi lattice, the transcendental lattice, the Mordell-Weil group and the Mordell-Weil lattice. This algorithm comes with a SageMath implementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line Pichon-Pharabod, Eric Algebraic Geometry Symbolic Computation Primary 14Q10, Secondary 32G20, 14D05 We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic invariants of the surface, notably the Néron-Severi lattice, the transcendental lattice, the Mordell-Weil group and the Mordell-Weil lattice. This algorithm comes with a SageMath implementation. |
| title | A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line |
| topic | Algebraic Geometry Symbolic Computation Primary 14Q10, Secondary 32G20, 14D05 |
| url | https://arxiv.org/abs/2401.05131 |