Singular Semi-Flat Calabi-Yau Metrics on S^2

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dc.creatorLoftin, John C.
dc.date2004-03-12
dc.date.accessioned2026-07-07T05:06:22Z
dc.date.available2026-07-07T05:06:22Z
dc.descriptionOn 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.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/math/0403218
dc.identifierhttp://arxiv.org/abs/math/0403218
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70443
dc.subjectDifferential Geometry
dc.subject32Q25; 53A15; 57M50
dc.titleSingular Semi-Flat Calabi-Yau Metrics on S^2
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