# extending biholomorphic maps to bimeromorphic maps

A meromorphic map of complex spaces (in the sense of Remmert) $f: X \to Y$ is a multivalued map such that its graph $\Gamma$ is an analytic subset of $X \times Y$ and off some analytic subset $Z \subset \Gamma$, the projection on the first coordinate is a biholomorphic map. If additionally, off some analytic subset, the projection on the second coordinate is biholomorphic the map is called bimeromorphic.

Let $X,Y$ be two compact complex spaces, $A$ and $B$ their analytic subsets, and let $f: X\setminus A \to Y\setminus B$ be a biholomorphic map. Is it always possible to extend $f$ to a bimeromorphic map between $X$ and $Y$?

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