Complex-analytic structures on moment-angle manifolds
Complex-analytic structures on moment-angle manifolds
复制标题
矩角流形上的复解析结构
DOI：
10.17323/1609-4514-2012-12-1-149-172
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Yuri Ustinovsky
中科院分区：
文献类型：
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作者：
T. Panov;Yuri Ustinovsky
证明了完全简单扇形所对应的矩角流形具有非kaehler复解析结构。这推广了已知的多面体弯角流形上复杂解析结构的构造，来自于将它们识别为lvm流形。利用全纯主束的Borel谱序列描述了矩角流形的Dolbeault上同调和一些Hodge数。
We show that the moment-angle manifolds corresponding to complete simplicial fans admit non-Kaehler complex-analytic structures. This generalises the known construction of complex-analytic structures on polytopal moment-angle manifolds, coming from identifying them as LVM-manifolds. We proceed by describing Dolbeault cohomology and some Hodge numbers of moment-angle manifolds by applying the Borel spectral sequence to holomorphic principal bundles over toric varieties.