Bando-Calabi-Futaki characters of Kähler orbifolds
Bando-Calabi-Futaki characters of Kähler orbifolds
复制标题
Kähler orbifolds 的 Bando-Calabi-Futaki 字符
DOI：
10.1007/s002080050299
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发表时间：
1999
影响因子：
1.4
通讯作者：
Y. Nakagawa
中科院分区：
文献类型：
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作者：
Y. Nakagawa
在本文中，我们一次性地固定了一个n维紧连通的复轨道dx和一个具有c1 (L)> 0的全纯线轨道-束-络- x（见[18]关于轨道和束的定义）。我们表示通过Aut◦(X)的身份组件组全纯orbifold-automorphisms (X)的李代数是认同了李代数H0 (X, O (T1 0 X))的全纯向量场在X T1 0 X的全纯切向量的向量orbifold-bundle类型(1,0)X召回,艾博年X的地图艾博年各种铝青铜(X)自然诱发李群同态αX: Aut◦(X)−→Aut◦(铝青铜(X))∼=铝青铜(X)。设GX为同态αX核的恒等分量，GX为对应的李子代数H0 （X, O (T1, 0X)）。然后，根据Fujiki[6]定理，GX具有线性代数群（定义在C上）的自然结构。此外，我们有
Throughout this paper, we fix once for all an n-dimensional compact connected complex orbifoldX and a holomorphic line orbifold-bundleLoverX with c1 (L)> 0 (see [18] for the definitions of an orbifold and an orbifoldbundle). We denote by Aut◦(X) the identity component of the group of holomorphic orbifold-automorphisms of X, whose Lie algebra is identified with the Lie algebra H0 (X, O (T1, 0X)) of holomorphic vector fields on X. Here T1, 0X is the holomorphic vector orbifold-bundle of tangent vectors of type (1, 0) on X. Recall that the Albanese map of X to the Albanese variety Alb (X) naturally induces a Lie group homomorphism αX: Aut◦(X)−→ Aut◦(Alb (X))∼= Alb (X).Let GX be the identity component of the kernel of the homomorphism αX, and gX the corresponding Lie subalgebra of H0 (X, O (T1, 0X)). Then, by a theorem of Fujiki [6], GX has a natural structure of a linear algebraic group (defined over C). Moreover, we have