Equisingular deformations of normal surface singularities. I
The author tackles the problem of defining equisingular infinitesimal deformations of normal singular points of algebraic surfaces \(S\). The technique is to study deformations of a resolution \(f: X\to S\) of the singularity \(x \in S\) which preserve the essential numerical (topological) data of the exceptional curve \(E=f^{-1}(x)\), and which blow down to deformations of \(S\). Much of this interesting paper consists of discussing the weaknesses as well as the strengths of this approach, for instance in comparison with the theory based on simultaneous blowing up along normally flat sections, which is generally more special than the authorts notion but coincides for certain well-studied classes of singularities.
scientific article; zbMATH DE number 3557922