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

中文翻译：

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用Picard-Fuchs算子计算刚性双octic Calabi-Yau三重的周期积分

我们提出了一种使用单参数平滑的 Picard-Fuchs 算子对刚性 Calabi-Yau 三重周期积分进行数值计算的方法。我们的方法提供了计算刚性双八边形周期积分晶格的可能性，而无需对其几何性质有任何明确的了解，仅使用 Fuchsian 方程理论和 MAPLE 中的计算的简单事实，并带有微分方程库。作为一个令人惊讶的结果，我们还得到了与所考虑的 Calabi-Yau 三重奇异（节点）模型相关的附加积分的近似值。