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- W912729150 abstract "Studying the invariants of isolated hypersurface germs f : (C, 0) → (C, 0), it is very useful to consider composed germs f = p ◦ φ, where φ : (C, 0) → (C, 0) has a manageable discriminant space (for example: φ is an isolated complete intersection singularity, in short ICIS), and p : (C, 0) → (C, 0) is a curve singularity. This gives not only a very large class of examples with powerful testing role (for example, the germs of “generalized Sebastiani– Thom type”, where φ(x, y) = (g(x), h(y)) [9, 10], or the topological series fk = pk ◦ φ → f∞ = p∞ ◦ φ, when φ is an ICIS and pk → p∞ is a topological series [10, 20] of plane singularities), but also clarifies the most general case. To see this, complete the initial, arbitrary germ f to an ICIS (f, g) = φ and take p(c, d) = c. If g is a generic linear form then we recover the classical method of the polar curves, which is an effective inductive procedure. In the composed case, the leading principal is the following: for a given invariant i, find a category C(i) of supplementary structures (“of system of coefficients”) defined either on (C, 0) or on the local complement of an analytic germ ∆ ⊂ (C, 0), (which, in general, is the discriminant space of φ) with the following properties: a) φ defines a structure S(φ) in C(i), and b) the invariant i(f) can be computed in terms of the germ p and the structure S(φ). In this way, one expects that the computation of the invariant i is reduced to lower dimensional topology (link topology of p−1(0)∪∆) with some repre-" @default.
- W912729150 created "2016-06-24" @default.
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- W912729150 date "1996-01-01" @default.
- W912729150 modified "2023-09-28" @default.
- W912729150 title "Variation structures: results and open problems" @default.
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