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arXiv · 2608.18432

Donaldson-Sun Theory in the Conic Case

Arka Karmakar
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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.

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Arka Karmakar. 2026-08-19. Donaldson-Sun Theory in the Conic Case. https://arxiv.org/abs/2608.18432

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