Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.
Adiabatic limits of Ricci-flat Kahler metrics
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abstract
We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau manifold which is the total space of a holomorphic fibration when the volume of the fibers goes to zero. By establishing some new a priori estimates for the relevant complex Monge-Ampere equation, we show that the Ricci-flat metrics collapse (away from the singular fibers) to a metric on the base of the fibration. This metric has Ricci curvature equal to a Weil-Petersson metric that measures the variation of complex structure of the Calabi-Yau fibers. This generalizes results of Gross-Wilson for K3 surfaces to higher dimensions.
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math.DG 1years
2026 1verdicts
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Special Lagrangian submanifolds and circle collapse on K3
Constructs degenerating special Lagrangian two-spheres and tori in collapsing K3 surfaces that lift from affine lines on a three-dimensional base, including connections between Taub-NUT bubbles.