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I'm trying to learn about the deformation theory of compact complex spaces. I'm familiar with the case of compact complex manifolds from the paper "On the Locally Complete Families of Complex Analytic Structures" by M. Kuranishi. The original references for the case of compact complex spaces seem to be the papers "Le problème des modules locaux pour les espaces $\mathbb C$-analytiques compacts" by A. Douady and "Der Satz von Kuranishi für kompakte komplexe Räume" by H. Grauert which are in French and German respectively.

Are there any English language references for the construction of versal deformations of compact complex spaces?

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    $\begingroup$ Try this one as a starter (in particular Chapter 4). $\endgroup$
    – MathCrawler
    Commented Aug 10, 2020 at 2:13
  • $\begingroup$ The title of Grauert's paper should read "Der Satz von Kuranishi für kompakte komplexe Räume". $\endgroup$
    – MathCrawler
    Commented Aug 10, 2020 at 7:52
  • $\begingroup$ Thanks for the correction and the reference! $\endgroup$
    – Mohan Swaminathan
    Commented Aug 10, 2020 at 12:09

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D. Barlet and J. Magnusson, Complex Analytic Cycles II. Unfortunately, the book is not in press at the moment, so you have to wait. While you wait, you can read Complex Analytic Cycles I.

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