Effective homology and periods of complex projective hypersurfaces
Algebraic Geometry
2026-02-03 v2 Symbolic Computation
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.
Keywords
Cite
@article{arxiv.2306.05263,
title = {Effective homology and periods of complex projective hypersurfaces},
author = {Pierre Lairez and Eric Pichon-Pharabod and Pierre Vanhove},
journal= {arXiv preprint arXiv:2306.05263},
year = {2026}
}
Comments
38 pages