Computing Periods of Hypersurfaces
Algebraic Geometry
2019-04-24 v2 Symbolic Computation
Abstract
We give an algorithm to compute the periods of smooth projective hypersurfaces of any dimension. This is an improvement over existing algorithms which could only compute the periods of plane curves. Our algorithm reduces the evaluation of period integrals to an initial value problem for ordinary differential equations of Picard-Fuchs type. In this way, the periods can be computed to extreme-precision in order to study their arithmetic properties. The initial conditions are obtained by an exact determination of the cohomology pairing on Fermat hypersurfaces with respect to a natural basis.
Cite
@article{arxiv.1803.08068,
title = {Computing Periods of Hypersurfaces},
author = {Emre Can Sertöz},
journal= {arXiv preprint arXiv:1803.08068},
year = {2019}
}
Comments
33 pages; Final version. Fixed typos, minor expository changes. Changed code repository link