Fibered Multilinks and singularities $f \bar g$

Details Fibered Multilinks and singularities $f \bar g$ Fibered Multilinks and singularities $f \bar g$

2005-05-15

arxiv.org/abs/math/0505312v1

Mathematics

Algebraic Geometry

Scientific paper

In this article we extend Milnor's fibration theorem for complex singularities to the case of singularities $f \bar g:(X,P) \to (C,0))$ defined on a complex analytic singularity germ $(X,P)$, with $f, g$ holomorphic and $f \bar g$ having an isolated critical value at $0 \in C$. This can also be regarded as a result for meromorphic germs. Then we strenghten this fibration theorem when $X$ has complex dimension 2, obtaining a fibration theorem for multilinks that extends previous work by Pichon. We prove that the multilink $L_{f \bar g}$ in $L_X$ (the link of $X$), is fibred iff the map $f \bar g$ has an isolated critical value at $0 \in C$, and in this case the map $\frac{f \bar g}{|f \bar g|}$ defined on $L_X \setminus L_{f \bar g}$ is a multilink fibration.We also give a combinatorial criterium, easy to verify, to decide when is $L_{f \bar g}$ a fibred multilink. We finally prove a realization theorem for fibred multilinks.

Affiliated with

Also associated with

No associations

Rating

Fibered Multilinks and singularities $f \bar g$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fibered Multilinks and singularities $f \bar g$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fibered Multilinks and singularities $f \bar g$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-4134