An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics
An L2-Poincaré–Dolbeault lemma of spaces with mixed cone-cusp singular metrics
复制标题
具有混合锥尖奇异度量的 L2-Poincaré-Dolbeault 引理空间
DOI：
10.1142/s1793525321500473
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发表时间：
2021-09
影响因子：
0.8
通讯作者：
Chen Zhao
中科院分区：
文献类型：
--
作者：
Junchao Shentu;Chen Zhao
具有锥尖混合奇点的Kähler爱因斯坦度量的存在性近年来受到了广泛的关注。人们相信这种度规会产生重要的几何不变量。我们在狄利克雷和诺伊曼边界条件下计算了它们的[公式：见原文]-Hodge-Frölicher谱序列，并在它们上面检验了纯霍奇结构。结果表明，这些上同调与良好紧化的de Rham上同调是一致的。
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 [Formula: see text]-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.