Related papers: Fibered Multilinks and singularities $f \bar g$
We study the boundary L_t of the Milnor fiber for the non-isolated singularities in C^3 with equation z^m - g(x,y) = 0 where g(x,y) is a non-reduced plane curve germ. We give a complete proof that L_t is a Waldhausen graph manifold and we…
The thesis deals with holomorphic germs $ \Phi: (\mathbb{C}^2, 0) \to (\mathbb{C}^3,0) $ singular only at the origin, with a special emphasis on the distinguished class of finitely determined germs. The results are published in two articles…
In analogy with the holomorphic case, we compare the topology of Milnor fibrations associated to a meromorphic germ f/g : the local Milnor fibrations given on Milnor tubes over punctured discs around the critical values of f/g, and the…
Given a nonconstant polynomial map over the reals having an isolated critical point in the origin and with zero locus of positive dimension, we establish a formula for the singular homology groups of a Milnor fibre relative to its boundary.
In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In…
Milnor fibrations were extended by Mutsuo Oka for certain mixed polynomial. In this paper, we study singular points of differentiable maps into the 2-dimensional torus, called Milnor fibration product maps, obtained by several Milnor…
Given a family of pairs of modules parametrised by a smooth space Y, the Multiplicity-Polar Theorem relates the multiplicity of the pair of modules at a special point of the parameter to the multiplicity of the pair at a generic point. This…
We study the topology of a line singularity, which is a complex hypersurface with non-isolated singularity given by a complex line. We describe the degeneration of its Milnor fibre to the singular hypersurface by means of a pair of…
We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to…
This paper applies the multiplicity polar theorem to the study of hypersurfaces with non-isolated singularities. The multiplicity polar theorem controls the multiplicity of a pair of modules in a family by relating the multiplicity at the…
In this paper, we study the topology of real analytic map-germs with isolated critical value $f: (\mathbb{R}^m,0) \to (\mathbb{R}^n,0)$, with $1 <n <m$. We compare the topology of $f$ with the topology of the compositions $\pi_i^* \circ f$,…
Milnor's fibration theorem and its generalizations play a central role in the study of singularities of complex and real analytic maps. In the complex analytic case, the Milnor fibration on the sphere is always given by the normalized map…
We consider suspension hypersurface singularities of type g=f(x,y)+z^n, where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for…
Let F be a fibration on a simply-connected base with symplectic fibre (M, \omega). Assume that the fibre is nilpotent and T^{2k}-separable for some integer k or a nilmanifold. Then our main theorem, Theorem 1.8, gives a necessary and…
Given a fibration in groupoids d : D -> I, we define a fibered multicategory as a particular functor p : M -> I, where M has the same objects as D, and its arrows a : X -> Y should be thought of as families of arrows in the multicategory,…
Let $\mathcal{F}$ be the germ at $\mathbf{0} \in \mathbb{C}^n$ of a holomorphic foliation of dimension $d$, $1 \leq d < n$, with an isolated singularity at $\mathbf{0}$. We study its geometry and topology using ideas that originate in the…
In this paper, we give some necessary and sufficient conditions for a normal subgroup of an amalgamated product of groups to be finitely generated. We apply these conditions together with Stallings' fibering theorem to prove that an…
We describe a new algebro-geometric perspective on the study of the Milnor fibration and, as a first step toward putting it into practice, prove powerful criteria for a deformation of a holomorphic function germ to admit a stratification on…
We study the fibration of augmented link complements. Given the diagram of an augmented link we associate a spanning surface and a graph. We then show that this surface is a fiber for the link complement if and only if the associated graph…
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…