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?