The Invariance of Milnor's Number Implies Topological Triviality
Copyright policy )The Invariance of Milnor's Number Implies Topological Triviality
THEOREM. Let F(z, t) be a polynomial in z = (z0, ... , zn) with coefficients which are smooth complex valued functions of t E RP such that F(O t) = 0, and for each t E RP, the polynomials aF/azi(z, t) in z have an isolated zero at 0. Assume moreover that the Milnor numbers ,t are independent of t, and that n # 2. Then for each parameter s E RP there exist a neighborhood U of (O, s) in CI' I x RP, Us of 0 in CI' I, and DI' of s in RP, and a homeomorphism a such that the diagram
Families, fibrations in algebraic geometry, Analytic subsets and submanifolds, Complex singularities, Singularities in algebraic geometry
Families, fibrations in algebraic geometry, Analytic subsets and submanifolds, Complex singularities, Singularities in algebraic geometry
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