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Title:
Ricci-flat Metrics on A_k Singularities
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Abstract:
By work of Gauntlett-Martelli-Sparks-Yau, the 3-dimensional A_k singularity admits no Ricci-flat Kähler cone metrics for k > 2. We show that if k > 3, then A_k admits a Ricci-flat Kähler metric with an isolated point singularity whose Gromov-Hausdorff tangent cone has nonisolated singularities. These new metrics also give rise to counterexamples to various open questions in the geometry of Ricci curvature. Joint work with Aaron Naber.
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