Computing periods of hypersurfaces
Copyright policy )Computing periods of hypersurfaces
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.
33 pages; Final version. Fixed typos, minor expository changes. Changed code repository link
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Variation of Hodge structures (algebro-geometric aspects), Analytic theory of abelian varieties; abelian integrals and differentials, Picard-Fuchs equations, Period matrices, variation of Hodge structure; degenerations, Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, 32G20, 14C30, 14D07, 14K20, 68W30, Griffiths-Dwork reduction, Mathematics - Algebraic Geometry, periods, Transcendental methods, Hodge theory (algebro-geometric aspects), Hodge theory, FOS: Mathematics, Algebraic Geometry (math.AG)
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Variation of Hodge structures (algebro-geometric aspects), Analytic theory of abelian varieties; abelian integrals and differentials, Picard-Fuchs equations, Period matrices, variation of Hodge structure; degenerations, Symbolic Computation (cs.SC), Symbolic computation and algebraic computation, 32G20, 14C30, 14D07, 14K20, 68W30, Griffiths-Dwork reduction, Mathematics - Algebraic Geometry, periods, Transcendental methods, Hodge theory (algebro-geometric aspects), Hodge theory, FOS: Mathematics, Algebraic Geometry (math.AG)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).13 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!