Donaldson-Sun Theory in the Conic Case

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.

Disclosure

“upport, and also for suggesting this topic. The author also thanks Colin Fan and Prof. Yuchen Liu for helpful discussions on algebraic geometry; especially the section on special test configurations. The author also acknowledges the use of GPT-5.6 Sol for proofreading and for assistance in developing the construction in Appendix A. The author takes full responsibility for all mathematical claims and any errors.”

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Classification

Brainstorming or outlining

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2

Verified

2026-08-22T18:32:14.720655Z

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