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Kahler spaces are just certain singular spaces equipped with a Kahler metric in appropriate sense. I first came across it Demaily-Paun's classical paper Numercical Characterization of the Kahler cone of a compact Kahler manifold. However it seems to refer the reader to the relevant background material in another paper of Demaily which is in French. I wonder whether there is any reference that have some background materials on Kahler spaces: definition, fundamental properties etc.

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There is a discussion of this topic in the recent book Cycles analytiques complexes II : l'espace des cycles by Barlet and Magnússon, chapter XII.3. An English translation (to be published by Springer) is forthcoming.

You will also find a short discussion in the book Degenerate Complex Monge–Ampère Equations by Guedj and Zeriahi, chapter 16.3.

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  • $\begingroup$ Thank you very much! By the way, since you mentioned Guedj and Zeriahi's book, is there any reference for the materials covered in their chapter 16 besides the standard references for minimal model program. Those seem to require too many prerequisites for differential geometers. $\endgroup$
    – penny
    Mar 18 at 14:56
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For a reference in English, you could take a look at this paper of Varouchas, which contains a definition of Kähler spaces and relatied concepts (e.g. Kähler morphisms) and some of their fundamental properties.

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  • $\begingroup$ Thank you very much! $\endgroup$
    – penny
    Mar 19 at 14:00

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