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Multiple point schemes for corank 1 maps. (English) Zbl 0691.58015

The authors consider corank 1 map germs f: (C\({}^ n,0)\to (C^ p,0)\) with \(p>n\). They discuss various ways to define multiple point schemes for such germs. These are used to give criteria for f to be stable or finitely determined. In the latter case, the multiple point schemes are isolated complete intersection singularities. The Milnor numbers of these (and of certain quotients) occur in formulas for the Euler characteristic of the image \(X_ t\) of a stable deformation of f, in case \(n=2\) or 3, \(p=n+1\).
Reviewer: J.H.M.Steenbrink

MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
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