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A Remark on a Theorem by Kodama and Shimizu

Isaev, Alexander


We prove a characterization theorem for the unit polydisc Δⁿ ⊂ ℂⁿ in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut (M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut (M) and Aut (Δⁿ ) are isomorphic as topological groups equipped with the compact-open topology, then M is holomorphically equivalent to Δⁿ.

CollectionsANU Research Publications
Date published: 2008-04-22
Type: Journal article
Source: Journal of Geometric Analysis
DOI: 10.1007/s12220-008-9026-y


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