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Fibrations associated with a pencil of plane curves. (Fibrations associées à un pinceau de courbes planes.) (French) Zbl 1030.32023
Let \(f\) and \(g\) be two holomorphic function germs at the origin \(\mathbb C^2.\)
The authors determine the set of atypical values of the pencil \(f_a=f+a g^n\colon (\mathbb C^2, o) \to \mathbb C\), where \(a\in \mathbb C\) and \(n \in \mathbb N^\ast.\) In fact, \(B\subset \mathbb C\) is finite and the pencil is equisingular over \(\mathbb C\setminus B.\) Then they compute irregular values at infinity of polynomial maps \(\mathbb C^2\to\mathbb C,\) study the Milnor fibration of all members of the pencil, and the characteristic polynomials in the pencil. In conclusion, in the case when \(g\) is a coordinate function, it is described the topology of the generic member of the pencil in terms of the minimal resolution of \(f\cdot g.\)
MSC:
32S55 Milnor fibration; relations with knot theory
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
32S15 Equisingularity (topological and analytic)
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