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MiS Preprint

Computing periods of hypersurfaces

Emre Sertöz


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.

MSC Codes:
32G20, 14C30, 14D07, 14K20, 68W30
Picard--Fuchs equations, Hodge theory, Griffiths--Dwork reduction, periods, algorithms

Related publications

2019 Repository Open Access
Emre Can Sertöz

Computing periods of hypersurfaces

In: Mathematics of computation, 88 (2019) 320, pp. 2987-3022