Bilinear forms and extremal Kähler vector fields associated with Kähler classes
Bilinear forms and extremal Kähler vector fields associated with Kähler classes
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DOI：
10.1007/bf01446626
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发表时间：
1995
影响因子：
1.4
通讯作者：
A. Futaki;T. Mabuchi
中科院分区：
文献类型：
--
作者：
A. Futaki;T. Mabuchi
本文对具有K/Ihler类7的n维紧致复连通流形X的HI‘i(X，IR)：=HI’i(X)AH2(X，IR)一次不动。对于任一复簇Y，我们用Aut~表示Y的全纯自同构群的单位分支，则X到Aib(X)的阿尔巴尼亚映射诱导出一个李群同态AX：Aut~~Aut~Alb(X)，且AX的核的单位分支G：=Ker~是线性代数群(见[4])。设Ru是G的幂等根，通过设置Kr：=G/Ru，我们得到一个约化代数群Kr，它是G/R的极大紧子群K的复化。然后，Chvalley分解允许我们得到一个代数群同构L：Kr-~ffKr CG，在G中直到共轭都是唯一的，使得它给正合列1~Ru~G-~Kr~1一个分裂，即G记为半直积
In this paper, we fix once for all an n-dimensional compact complex connected manifold X with a K/ihler class 7 E HI'I (X, IR):= HI'I (x) AH2 (X, IR). For any complex variety Y, we denote by Aut~ the identity component of the group of holomorphic automorphisms of Y. Then the Albanese map of X to the Albanese variety AIb (X) induces a Lie group homomorphism ax: Aut~~ Aut~ Alb (X)), and the identity component G:= Ker~ of the kernel of ax is a linear algebraic group (see [4]). Let Ru be the unipotent radical of G, and by setting Kr:= G/Ru, we have a reductive algebraic group Kr which is a complexification of a maximal compact subgroup K of G/R,. Then the Chevalley decomposition allows us to obtain an algebraic group isomorphism l: Kr-~ ffKr CG, unique up to conjugacy in G, such that it gives a splitting to the exact sequence 1~ Ru~ G--~ Kr~ 1, ie, G is written as a semidirect product