Dolbeault cohomologies of blowing up complex manifolds II: Bundle-valued case
Dolbeault cohomologies of blowing up complex manifolds II: Bundle-valued case
复制标题
炸毁复流形的 Dolbeault 上同调 II：束值情况
DOI：
10.1016/j.matpur.2019.02.010
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发表时间：
2020
影响因子：
2.3
通讯作者：
Yang Xiangdong
中科院分区：
文献类型：
--
作者：
Rao Sheng;Yang Song;Yang Xiangdong
利用层理论的方法，得到了紧致复流形上具有全纯向量丛的Dolbeault上同调群的爆破公式。作为应用，我们给出了几个与Girbau、Kawamata-Viehweg和Green-Lazarsfeld的消失定理相关的正(负)例子，并研究了一些经典全纯不变量的爆破不变性。
We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples associated to the vanishing theorems of Girbau, Kawamata–Viehweg, and Green–Lazarsfeld in a uniform manner and study the blow-up invariance of some classical holomorphic invariants.