Sur la topologie d'une famille de pinceaux de germes d'hypersurfaces complexes

Variation of the Milnor Fibration in Pencils of Hypersurface Singularities

“…This is a short version of my PhD thesis [3], a summary of which has already been published in [4]. I thank my advisor, Franc Ëoise Michel, for many useful discussions.…”

“…Sketch of proof (see [3] for details). This is a consequence of the fact that, for every neighbourhood…”

“…But the facts that the critical locus Crit F is a curve, and that J t has an isolated singularity, imply that t is of Type II and then that its Milnor ®bre is obtained from that of a transverse member J trans by attaching some n-handles (see [3,III.3.2] for a more detailed discussion). Their Euler characteristics are then different.…”

“…We will illustrate our methods by computing the Milnor number of this generic member J gen f g. See also [1]. For details, see [3]. The Milnor ®bres of f , g and f g will be denoted by F f , F g and F gen , respectively.…”

Hypersurface Singularities and Milnor Equisingularity

“…The swing has also been studied in [3], [29], [17], [31]. However, no detailed proof of the swing has appeared in the literature.…”