A result of Artin states that analytification of proper algebraic spaces over $\mathbb{C}$ defines an an equivalence of the category of proper algebraic spaces with the category of Moishezon spaces. Is there some way to make sense algebro-geometrically of compact complex-analytic spaces of lower algebraic dimension?

  • $\begingroup$ For the maximal meromorphic quotient $f:X\to Y$ with $Y$ algebraic, presumably you can think of $X$ as the pullback over $Y$ of the tautological family of complex analytic spaces for the natural meromorphic map from $Y$ to the Douady space of the fibers of $f$. $\endgroup$ – Jason Starr Dec 27 '18 at 17:13

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