I'm looking for references on the proof (due to B. Moishezon, I guess) that any Moishezon space becomes a projective smooth complex variety after a finite number of blow-ups (called a modification?) His own articles on this that I could find are mainly in Russian, except a few survey papers (in English) without too much proof. I don't read Russian. 


Could anyone give some references in English/French? Also, since I didn't read Moishezon's original paper, I don't know the precise statement for this result (e.g. if one can impose some constraints on the subspaces that we blow up). Can someone give the precise statement?



References on Moishezon spaces in English/French
Dear Shenghao,


I) I am happy to report that according to Ueno's *Classification of Algebraic Varieties and Compact Complex Spaces*, Springer LNM 439, 1975, Moishezon's papers have been translated into English : AMS Translation Ser.2, *63* (1967), 51-177.


II) Here is the precise statement you request. Given a Moishezon variety $X$, you can obtain a smooth projective manifold $\tilde X$ from it by a finite succession of blowing-ups and the canonical morphism between their meromorphic function fields 
$\mathcal M (X) \to \mathcal M (\tilde {X})$ is an isomorphism of fields. If $X$ is smooth, the blow-ups can be taken with smooth centers. 


III) And finally two facts you probably already know.


a) A Moishezon manifold is projective algebraic iff it is Kähler.


b) A smooth Moishezon *surface* , i.e. manifold of dimension two, is automatically projective. This is a theorem by Chow and Kodaira ( proved long before Moishezon introduced his general definition ). 


