AI 中文总结
将Donaldson-Sun度量切锥理论推广到边界系数为有理数有限子集的锥Kähler-Einstein对的非塌缩Gromov-Hausdorff极限，证明对数度量切锥的唯一性，关联稳定退化机制，构造反例表明Kähler-Einstein假设对切锥刚性的必要性。
AI 中文摘要
我们将Donaldson-Sun的度量切锥理论推广到锥Kähler-Einstein对的非塌缩Gromov-Hausdorff极限情形，该对的边界系数属于有理数集的一个固定有限子集，且证明了对数度量切锥的唯一性。此外，在温和的lc相容性条件下，我们将其与Li-Xu及Li-Liu-Xu的稳定退化机制关联起来。我们还在CP²上构造了带一致下Ricci界且体积非塌缩的极化光滑Kähler度量，其极限具有非唯一的切锥，表明Kähler-Einstein假设对刚性是至关重要的。
英文摘要
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.
