2009/07/09 by Julien Keller, Keller, Julien, Sergio Lukić +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.0907.1387
openalex publication_date 2009/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a simple and very fast algorithm that computes Weil-Petersson\nmetrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using\nDonaldson's quantization link between the infinite and finite dimensional G.I.T\nquotients that describe moduli spaces of varieties, we define a natural\nsequence of Kaehler metrics. We prove that the sequence converges to the\nWeil-Petersson metric. We also develop an algorithm that numerically\napproximates such metrics, and hence the Weil-Petersson metric itself. Explicit\nexamples are provided on a family of Calabi-Yau Quintic hypersurfaces in CP4.\nThe scope of our second algorithm is much broader; the same techniques can be\nused to approximate metrics on null spaces of Dirac operators coupled to\nHermite Yang-Mills connections.\n