Numerical Calabi-Yau metrics

Abstract

We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics, and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results.

23 pages, 3 figures

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• Numerical Ricci-flat metrics on K3
• Notes on GIT and symplectic reduction for bundles and varieties
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