The Moduli Space of Kähler Structures on a Real Compact Symplectic Manifold
The Moduli Space of Kähler Structures on a Real Compact Symplectic Manifold
复制标题
实紧辛流形上凯勒结构的模空间
DOI：
10.2977/prims/1195175329
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
G. Schumacher
中科院分区：
文献类型：
--
作者：
A. Fujiki;G. Schumacher
都是足够大的k。因此空间^* 是复Hilbert解析空间通过拓扑群的等价物，拓扑群是真实的Hilbert流形。我们证明这些行动是适当的（定理30 3）。我们把Ji^看作是Jt^的逆极限，具有诱导Hausdorff拓扑。它包含Kahler结构的不允许非零全纯向量场的开子空间Ji'm。我们的主要结果（定理6 B 9）说明Jt ′（limJt）自然是一个ILH-V-空间。e0 Jt '0是ILH-空间与有限群的局部商。这里一个ILH-空间本质上是一个在Omori [OM]意义下具有奇点的ILH-流形。主要定理的证明主要基于2 m作用于9%>的ILH范畴中的切片的构造。
all sufficiently large k. Therefore the spaces ^* are quotients of complex Hilbert analytic spaces by topological groups which are real Hilbert manifolds. We prove that these actions are proper (Theorem 30 3). We view Ji^ as the inverse limit of Jt^ with the induced Hausdorff topology. It contains the open subspace Ji'm of Kahler structures which admit no nonvanishing holomorphic vector fields. Our main result (Theorem 6B 9) states that Jt'^limJt^ is naturally an ILH-V-space3 i. e0 Jt'0 is locally a quotient of an ILH-space by a finite group. Here an ILH-space is essentially an ILH-manifold in the sense of Omori [OM] with singularities. The proof of the main theorem is mainly based upon the construction of slices in the ILH-category for the action of 2m on 9%>