Related papers: Fibrations of highly singular map germs

In this paper, we study rigidity of nonsingular del Pezzo fibrations over a germ of smooth curve.

We prove that every map-germ ${f \bar g}: (\C^n,\0) {\to}(\C,0)$ with an isolated critical value at 0 has the Thom $a_{f \bar g}$-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs $f \bar g$ and it…

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of…

We investigate the regularising properties of singular kernels at the level of germs, i.e. families of distributions indexed by points in $\mathbb{R}^d$. First we construct a suitable integration map which acts on general coherent germs.…

This article first answers to questions about connectedness of a new family of graphs on unicellular maps. Answering these questions goes through a description of the mapping class group as surgeries on unicellular maps. We also show how…

We give examples of local signatures, completely different from the usual ones, for general fibrations of genus $2$ and genus $3$.

We give an algorithm to classify singular fibers of finite cyclic covering fibrations of a ruled surface by using singularity diagrams. As the first application, we classify all fibers of 3-cyclic covering fibrations of genus 4 of a ruled…

In this article we prove that a semialgebraic map is a branched covering if and only if its associated spectral map is a branched covering. In addition, such spectral map has a neat behavior with respect to the branching locus, the…

An extremal curve germ is a germ of a threefold $X$ with terminal singularities along a connected reduced complete curve~$C$ such that there exists a $K_X$-negative contraction $f : X \to Z$ with~$C$ being a fiber. We give a rough…

This paper classifies Lagrangian fibrations over surfaces with compact total spaces up to fiberwise symplectomorphism identical on the base.

We prove that for a fibration of simply-connected spaces of finite type $F\hookrightarrow E\to B$ with $F$ being positively elliptic and $H^*(F,\qq)$ not possessing non-trivial derivations of negative degree, the base $B$ is formal if and…

Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result…

In this article we extract and study the zero entropy subfamilies of a certain family of birational maps of the plane. We find these zero entropy mappings and give the invariant fibrations associated to them.

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to…

We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the…

We consider a proper flat fibration with real base and complex fibers. First we construct odd characteristic classes for such fibrations by a method that generalizes constructions of Bismut-Lott. Then we consider the direct image of a…

In this paper, we discuss the concept of $\rho$-regularity of analytic map germs and its close relationship with the existence of locally trivial smooth fibrations, known as the Milnor fibrations. The presence of a Thom regular…

It is well-known that for certain local connectivity assumptions the fundamental groupoid of a topological space can be equipped with a topology making it a topological groupoid. In other words, the fundamental groupoid functor can be…

In order to deduce the internal version of the Brown exact sequence from the internal version of the Gabriel-Zisman exact sequence, we characterize fibrations and $\ast$-fibrations in the 2-category of internal groupoids in terms of the…

Let $M$ be a smooth surface in $\mathbb R^3$ (or a complex surface in $\mathbb C^3$) and $k\geq 2$ be an integer. At any point on $M$ and for any plane in $\mathbb R^3$, we construct a holomorphic map-germ $(\mathbb C^2,0)\to(\mathbb…