Year: 2026
Type: preprint
Abstract: We extend the Donaldson-Sun theory of metric tangent cones to non-collapsing Gromov-Hausdorff limits of conical Kahler-Einstein pairs whose boundary coefficients lie in a fixed finite subset of Q, and prove uniqueness of the log metric tangent cone. Furthermore, under a mild lc compatibility condition, we relate this with the Li-Xu and Li-Liu-Xu stable degeneration machinery. We also construct polarized smooth Kaehler metrics on CP^2 with a uniform lower Ricci bound and volume non-collapsing, whose limit has nonunique tangent cones, showing that the Kahler-Einstein assumption is crucial for rigidity.
Source: arXiv (Cornell University)
Author: Karmakar, Arka
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203875802
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