Abstract: We present rigorous computation of Calabi-Yau manifold periods using Picard-Fuchs differential equations and high-precision arithmetic (50-digit precision). Implementing actual Frobenius series solutions and Wronskian-based verification, we compute the 4 periods of the mirror quintic (h2,1 = 1) and verify their linear independence. We validate the correct period formula b3 = 2h2,1 + 2 (the dimension of middle cohomology) against known mathematical literature. All computations are performed numerically using mpmath with 50-digit precision, providing verifiable numerical evidence for period independence. We present this as a computational foundation for more rigorous Hodge conjecture analysis.
Matthew Ulrey (Thu,) studied this question.
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