The existence of Kähler Einstein metrics with mixed cone and cusp singularity has received considerable attentions in recent years. It is believed that such kind of metric would give rise to important geometric invariants. We computed their L2-Hodge–Frölicher spectral sequence under the Dirichlet and Neumann boundary conditions and examine the pure Hodge structures on them. It turns out that these cohomologies agree well with the de Rham cohomology of a good compactification.

中文翻译：

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具有混合锥尖奇异度量的空间的 L2-Poincaré-Dolbeault 引理

近年来，具有混合锥和尖点奇点的 Kähler Einstein 度量的存在受到了相当多的关注。相信这种度量会产生重要的几何不变量。我们计算了他们的大号2-Dirichlet 和 Neumann 边界条件下的 Hodge-Frölicher 谱序列，并检查其上的纯 Hodge 结构。事实证明，这些上同调与良好紧化的 de Rham 上同调很好地吻合。