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Let $X$ be a holomorphically convex manifold, namely, for any infinite discrete subset of $X$ there exists a holomorphic function on $X$ which is unbounded on this set, then a theorem of Remmert says that there is a Stein space $X'$ and a proper holomorphic map $f:X\rightarrow X'$ such that $f_*\mathcal O(X)=\mathcal O(X')$.

Question: Is there any result about the property of the singularity of $X'$? For example, is the embedding dimension of $X'$ always finite?

Thanks a lot for your help!

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The Cartan Remmert reduction can be any normal Stein space.By a theorem of Bingener and Flenner Arch Math (Basel)32(1979) pages 34-37 One can construct normal Stein spaces with unbounded embedding dimension .Any smooth resolution of this normal space will have this normal space as its Cartan Remmert reduction.

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