Numerical Calabi–Yau metrics

2006/12/11 by Michael R. Douglas, Robert L. Karp, Sergio Lukić +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Calabi–Yau manifold #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematics #Pure mathematics #hep-th

paper · pdf · doi:10.1063/1.2888403

published as J.Math.Phys.49:032302,2008 · 23 pages, 3 figures

arxiv created 2006/12/11 · openalex publication_date 2008/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Principles of Algebraic Geometry
• Scalar Curvature and Projective Embeddings, I
• Number variance of random zeros
• Some numerical results in complex differential geometry
• Numerical Ricci-flat metrics on K3
• Distribution of Zeros of Random and Quantum Chaotic Sections of Positive Line Bundles
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I

Cited by

• Calabi-Yau metrics for quotients and complete intersections
• Yukawa textures from heterotic stability walls