Fibrations associated with a pencil of plane curves
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 \(f\cdot g.\)
scientific article; zbMATH DE number 1911466