2005/06/30 by Matthew Headrick, Toby Wiseman · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1088/0264-9381/22/23/002
published as Class.Quant.Grav. 22 (2005) 4931-4960 · 38 pages, 10 figures; program code and animations of figures downloadable from http://schwinger.harvard.edu/~wiseman/K3/ ; v2 minor corrections, references added
openalex publication_date 2005/11/09 · arxiv created 2006/04/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T4/Z2 orbifold with many discrete symmetries. High-resolution metrics may be obtained on a time scale of days using a desktop computer. We compute various geometric and spectral quantities from our numerical metrics. Using similar resources we expect our methods to practically extend to Calabi-Yau three-folds with a high degree of discrete symmetry, although we expect the general three-fold to remain a challenge due to memory requirements.