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Title:
Stability and boundedness of klt singularities III
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Abstract:
Donaldson and Sun showed that singularities on Gromov-Hausdorff limits of Kähler-Einstein Fano manifolds have algebraic metric tangent cones, and they conjectured that these metric tangent cones only depend on the algebraic structure of the singularities. In the study of this conjecture, Li and Xu proposed the Stable Degeneration Conjecture, predicting that every klt singularity has a canonical “stable degeneration” induced by the valuation with smallest normalized volume. In my talks, I’ll introduce some related backgrounds, survey the recent solution of these conjectures, and discuss some implications on boundedness of singularities.
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