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Topological invariants of \(\mu\)-constant deformations of complete intersection singularities. (English) Zbl 0724.32019
The main results of the reviewing article concern germs \(f\) which are semi-weighted homogeneous or nondegenerate in the sense of Khovanskii [see A. G. Khovanskii, Funct. Anal. Appl. 11, 289–296 (1978); translation from Funkts. Anal. Prilozh. 11, No. 4, 56–64 (1977; Zbl 0445.14019)]. For an unfolding \(F(x,u)=(\bar F(x,u),u)\) of \(f\) on non-decreasing weight or filtration it is proved that \(F\) is topologically trivial for contact equivalence, so \(\bar F^{-1}(0)\) is a topologically trivial deformation of \(V_ 0=f^{-1}(0)\), and the principal type and principal monodromy for a direction is topologically constant under such deformations. Even though the discriminant may change under such unfoldings at least part of the monodromy must remain constant. In the complex case for two such germs with either the same weights or Newton polyhedra the following assertions are true: they are topologically contact equivalent, any common principal types are topologically equivalent, and any common principal monodromy agree.

32S30 Deformations of complex singularities; vanishing cycles
32S05 Local complex singularities
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