Compact singularities of meromorphic mappings between complex 3-dimensional manifolds (Q5929471)

The main result of this paper is the following extendibility theorem for equidimensional meromorphic mappings: Let \(M\) be a Stein 3-manifold and \(X\) be a compact complex 3-manifold, let \(K\) be a compact set with connected complement in \(M\) and let \(f: M \setminus K \to X\) be a meromorphic mapping, then there exists a finite set \(A=\{ a_1,\dots,a_d \} \subset K\) such that: 1) \(f\) has a meromorphic extension \(\widehat{f}: M \setminus A \to X\); 2) for every coordinate ball \(B(a_j)\) satisfying \(\partial B(a_j) \bigcap A =\emptyset\), \(\widehat{f}(\partial B(a_j))\) is not homologous to zero in \(X.\) In particular, if \(X\) is simply connected, then the mapping \(f\) extends to all of \(M\).NEWLINENEWLINENEWLINEThere are also some generalizations made and open questions raised.