Variation of the Milnor fibration in pencils of hypersurface singularities (Q2766420)

Let \(f\) and \(g\) be holomorphic function germs on \( ({\mathbb C}^{n+1}, 0)\) without common factor. The author studies pencils of germs of complex hypersurfaces \(\varphi_\tau = \alpha g - \beta f\), \(\tau = (\alpha : \beta) \in {\mathbb P}^1.\) He proves that all transverse members of the pencil with no blowing up [see \textit{J. P. Henry}, et al., Ann. Sci. Éc. Norm. Supér., IV. Sér. 17, 227-268 (1984; Zbl 0551.32012)] have isotopic Milnor fibrations. Furthermore, every non-transverse member of such a pencil has a Milnor subfibration isotopic to a Milnor subfibration of every transverse member. NEWLINENEWLINENEWLINESome applications to the study of generalized Iomdine-Lê deformations and of the Malgrange pencil [\textit{B. Malgrange}, Invent. Math. 20, 171-172 (1973; Zbl 0264.14003)] are considered in detail. The paper under review is an expanded version of the note [\textit{C. Caubel}, C. R. Acad. Sci., Paris, Sér. I, Math. 328, 501-504 (1999; Zbl 0956.32026)], a brief account of the main results of the author's PhD thesis.