Kähler–Einstein metrics near an isolated log-canonical singularity
Kähler–Einstein metrics near an isolated log-canonical singularity
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DOI：
10.1515/crelle-2022-0095
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
V. Datar;X. Fu;Jian Song
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文献类型：
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作者：
V. Datar;X. Fu;Jian Song
摘要本文在孤立对数正则（非对数终端）奇点附近构造具有负标量曲率的Kähler-Einstein度量。如果底层空间具有复杂的维度2，那么这些度量在奇点附近是完整的。我们还建立了Kähler-Einstein指标在某些类型的孤立对数正则奇点附近的稳定性结果。作为应用，对于复维2对数正则奇点，我们证明了在孤立对数正则（非对数终端）奇点附近的任何负标量曲率的完备Kähler-Einstein度规平滑渐近地接近双曲几何模型Kähler-Einstein度规。
Abstract We construct Kähler–Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2. We also establish a stability result for Kähler–Einstein metrics near certain types of isolated log canonical singularity. As application, for complex dimension 2 log canonical singularity, we show that any complete Kähler–Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to model Kähler–Einstein metrics from hyperbolic geometry.