Effective homology and periods of complex projective hypersurfaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918318219198464 |
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| author | Lairez, Pierre Pichon-Pharabod, Eric Vanhove, Pierre |
| author_facet | Lairez, Pierre Pichon-Pharabod, Eric Vanhove, Pierre |
| contents | We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwine with a new method for computing an explicit basis of the singular homology of the hypersurface. It is based on Picard-Lefschetz theory and relies on the computation of the monodromy action induced by a one-parameter family of hyperplane sections on the homology of a given section. We provide a SageMath implementation. For example, on a laptop, it makes it possible to compute the periods of a smooth complex quartic surface with hundreds of digits of precision in typically an hour. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05263 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective homology and periods of complex projective hypersurfaces Lairez, Pierre Pichon-Pharabod, Eric Vanhove, Pierre Algebraic Geometry Symbolic Computation Primary 14Q15, Secondary 32G20, 14D05 We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwine with a new method for computing an explicit basis of the singular homology of the hypersurface. It is based on Picard-Lefschetz theory and relies on the computation of the monodromy action induced by a one-parameter family of hyperplane sections on the homology of a given section. We provide a SageMath implementation. For example, on a laptop, it makes it possible to compute the periods of a smooth complex quartic surface with hundreds of digits of precision in typically an hour. |
| title | Effective homology and periods of complex projective hypersurfaces |
| topic | Algebraic Geometry Symbolic Computation Primary 14Q15, Secondary 32G20, 14D05 |
| url | https://arxiv.org/abs/2306.05263 |