Abstract
Let B0 be a local singularity of dimension d. Then we consider the problem of Lech, whether for every deformation (A,m) −→ (B,n) of B0 the inequality H A ≤ H1 B between the Hilbert functions is true, and give a positive answer in the case, that the formal versal deformation of B0 is a base change of an algebraic family (R,M) −→ (S, N), where R is regular and dim S = dim R + d. So one should lift versal deformations in that way. There are obstructions against this in certain second Harrison cohomology groups. This research was carried out during a stay at Max-Planck-Institut fur Mathematik at Bonn. The financial support and hospitality of this institute are greatfully acknowledged by the author. Personally he would like to thank B. Herzog (Stockholm) for the introduction to that kind of problems and F. Patras for the stimulating conversation on Harrison cohomology.
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