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Zbl 0751.14022
Altmann, Klaus
Equisingular deformations below the Newton boundary. (English)
[J] Compos. Math. 80, No.3, 257-283 (1991). ISSN 0010-437X; ISSN 1570-5846/e

The author considers equisingular deformations and embedded equisingular deformations of germs of surface singularities $f=0$ in $k\sp 3$ $(k$ algebraically closed, $\text{char}(k)=0)$, $f$ being assumed to be non degenerated on its Newton boundary. It is shown that any equisingular first-order deformation $\xi$ may be split in equisingular parts $\xi=\xi\sb 1+\xi\sb 3+\xi\sb 3$, each $\xi\sb i$ being induced by an equisingular deformation of an embedded resolution. Furthermore, first order deformations induced by the embedded equisingular ones relative to a fixed embedded resolution are characterized. Both results give rise to an algorithm for computing all equisingular first order deformations in the whole of first order deformations of the germ.
[E.Casas-Alvero (Barcelona)]

MSC 2000:: *14J17 Singularities of surfaces
14B05 Singularities (algebraic geometry)
14B07 Deformations of singularities (local theory)

Keywords: embedded equisingular deformations of germs of surface singularities; computing equisingular deformations; embedded equisingular deformations of germs of surface singulrities

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