A global morphism from the Douady space to the cycle space - Magnússon, Jón Ingólfur (MATHEMATICA SCANDINAVICA, 2007)
We establish, for any given complex space M, a global morphism from the reduction of its Douady space to its cycle space. This morphism is an extension of the morphism defined in [1] from the subspace of the Douady space formed by all pure dimensional subspaces of M to the cycle space of M. In the case where M is projective this morphism is the classical morphism from the Hilbert scheme of M to the Chow scheme of M.