Computing period integrals of rigid double octic Calabi-Yau threefolds\n with Picard-Fuchs operator

2019/10/11 by Tymoteusz Chmiel, Chmiel, Tymoteusz
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1910.05218

openalex publication_date 2019/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a method for numerical computation of period integrals of a rigid\nCalabi-Yau threefold using Picard-Fuchs operator of a one-parameter smoothing.\nOur method gives a possibility of computing the lattice of period integrals of\na rigid double octic without any explicit knowledge of its geometric\nproperties, employing only simple facts from the theory of Fuchsian equations\nand computations in MAPLE with a library for differential equations. As a\nsurprising consequence we also get approximations of additional integrals\nrelated to a singular (nodal) model of considered Calabi-Yau threefold.\n

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