Finiteness of some families of meromorphic maps (Q1112210)

H. Cartan proved that there are at most two distinct nonconstant meromorphic functions on \({\mathbb{C}}\) which have the same inverse images with multiplicites counted for three distinct value. The author [Nagoya Math. J. 83,153-181 (1981; Zbl 0431.32032)] extended this result for several complex variables. He gives here a generalization of it for meromorphic mappings of a compact complex manifold minus a thin set into an projective algebraic manifold.