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

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

2004-03-12

arxiv.org/abs/math/0403218v1

Mathematics

Differential Geometry

25 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Singular Semi-Flat Calabi-Yau Metrics on S^2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singular Semi-Flat Calabi-Yau Metrics on S^2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular Semi-Flat Calabi-Yau Metrics on S^2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-686550