Locally trivial displacements of analytic subvarieties with ordinary singularities (Q1080003)

The author announces the following result: Let \(i: Z\to Y\) be the inclusion of an irreducible complex subspace into a compact complex manifold. Assume that Z has ordinary singularities, i.e. the total space X of the normalization \(\nu\) : \(X\to Z\) is smooth and \(f=i\circ \nu: X\to Y\) is infinitesimally stable. Then the functors of a) locally trivial embedded deformations of Z in Y and of b) deformations of the map \(f: X\to Y\) have semiuniversal objects and are equivalent.