Equivariant deformations of meromorphic actions on compact complex manifolds
Equivariant deformations of meromorphic actions on compact complex manifolds
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紧复流形上亚纯作用的等变变形
DOI：
10.1007/pl00004443
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发表时间：
2001
影响因子：
1.4
通讯作者：
N. Honda
中科院分区：
文献类型：
--
作者：
N. Honda
抽象的。杂态性是全态最基本的特性
$ {\ mathbb c}^*$ - 紧凑型复杂歧管上的动作。我们证明
如果复杂歧管的复杂维度大于两个，则$ {\ mathbb c}^*$ - 紧凑复合歧管上的动作不一定由小变形保留。相比之下，我们还表明
$ {\ mathbb c}^*$ - 紧凑型复杂表面上的动作仅取决于表面的拓扑（第一个betti编号）。我们通过研究某些复合物的三倍（所谓的扭曲器空间）的模棱两可的变形来构建大于两个尺寸的示例。
Abstract. Meromorphicity is the most basic property for holomorphic
${\mathbb C}^*$-actions on compact complex manifolds. We prove that the meromorphicity of
${\mathbb C}^*$-actions on compact complex manifolds are not necessarily preserved by small deformations, if the complex dimension of complex manifolds is greater than two. In contrast, we also show that the meromorphicity of
${\mathbb C}^*$-actions on compact complex surface depends only on the topology (the first Betti number) of the surface. We construct such examples of dimension greater than two by studying an equivariant deformation of certain complex threefold, so called a twistor space.