A meromorphic map of complex spaces (in the sense of Remmert) f:X→Y is a multivalued map such that its graph Γ is an analytic subset of X×Y and off some analytic subset Z⊂Γ, 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 projective complex spaces, A and B their analytic subsets, and let f:X∖A→Y∖B be a biholomorphic map. Is it always possible to extend f to a bimeromorphic map between X and Y?

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 projective 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 $Y$?