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arXiv · 2306.05263

Effective homology and periods of complex projective hypersurfaces

Pierre Lairez·Eric Pichon-Pharabod·Pierre Vanhove
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Abstract

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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Pierre Lairez, Eric Pichon-Pharabod, Pierre Vanhove. 2023-06-08. Effective homology and periods of complex projective hypersurfaces. https://doi.org/10.1090/mcom/3947

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