Abstract
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%><B
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