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Singular Semi-Flat Calabi-Yau Metrics on S^2 | | John C. Loftin
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12 Mar 2004 | | Subject: | Differential Geometry MSC-class: 32Q25; 53A15; 57M50 | math.DG | | Abstract: | On an affine flat manifold with coordinates x^j and convex local potential function f, we call the affine Kahler metric f_{ij} dx^i dx^j semi-flat Calabi-Yau if it satisfies det f_{ij} = 1. Recently Gross-Wilson have constructed many such metrics on S^2 minus 24 singularities, as degenerate limits of Calabi-Yau metrics on elliptic K3 surfaces. We construct many more such metrics on S^2, singular at any 6 or more points, and compute the local affine structure near the singularities. The techniques involve affine differential geometry and solving a semilinear PDE on S^2 minus singularities. We also compute the action mirror symmetry should have on the resulting surfaces. | | Source: | arXiv, math.DG/0403218 | | Services: | Forum | Review | PDF | Favorites | |
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