Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II

Abstract

We study non-collapsed Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below. Our main result is that each tangent cone is homeomorphic to a normal affine variety. This extends a result of Donaldson-Sun, who considered non-collapsed limits of polarized Kähler manifolds with two-sided Ricci curvature bounds.

arXiv comment18 pages, error on formula (3.16) corrected

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Cited by in corpus (5)

• Kähler manifolds with almost non-negative curvature
• Conjectures and Open Questions on the Structure and Regularity of Spaces with Lower Ricci Curvature Bounds
• On the Ohsawa-Takegoshi extension theorem
• An explicit estimate of the Bergman kernel for positive line bundles
• Metric rigidity of Kahler manifolds with lower Ricci bounds and almost maximal volume