Effective homology and periods of complex projective hypersurfaces
Overview & Synopsis
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
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Document Information
| Document Title | Effective homology and periods of complex projective hypersurfaces |
|---|---|
| Author / Organization | Pierre Lairez, Eric Pichon-Pharabod, Pierre Vanhove |
| Subject & Discipline | Multidisciplinary Academic Open Research |
| Categories | Science & Mathematics |
| Publication Year | 2024 |
| License / Rights | Open Access / Creative Commons |
| Resource Verification | Listed PDF (Verification Pending) |
| Original Host Website |
HAL Open Science
(hal.science)
|
| File Format | application/pdf (Portable Document Format) |
| Language | EN |
| Catalog ID | DOC-92245 |
| Original Source Link | Visit Source Page on hal.science » |