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Numerical Metrics, Curvature Expansions and Calabi-Yau Manifolds
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We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the validity of curvature expansions in string effective theories. Nevertheless, for seemingly generic points in moduli space it can be difficult to analytically determine if there might be a highly curved region localized somewhere on the Calabi-Yau manifold. We show that numerical techniques are rather efficient at deciding this issue.
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Approximate Ricci-flat Metrics for Calabi-Yau Manifolds
Analytic approximate Ricci-flat Kähler potentials are obtained for one-parameter Dwork quintic and bi-cubic Calabi-Yau three-folds by fitting Donaldson's Ansatz to machine-learned numerical metrics.
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