Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x)

Details Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x) Topological Triviality of $μ$-constant Deformations of Type f(x) + tg(x)

1997-11-11

arxiv.org/abs/alg-geom/9711014v1

Mathematics

Algebraic Geometry

AMS-LaTeX, 7 pages

Scientific paper

We show that every $\mu$-constant family of isolated hypersurface singularities of type f(x) + tg(x), where t is a parameter, is topologically trivial. In the proof we construct explicitely a vector field trivializing the family. The proof uses only the curve selection lemma and hence, for an appropriately translated statement, also works over the reals. Some applications to the study of singularities at infinity of complex polynomials are given.

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