Related papers: Fibrations of highly singular map germs

We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of…

The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of…

We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every…

We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a polynomially bounded o-minimal structure over the reals, surface germs. In particular, any definable H\"older triangle is either Lipschitz normally…

In this survey on local additive invariants of real and complex definable singular germs we systematically present classical or more recent invariants of different nature as emerging from a tame degeneracy principle. For this goal, we…

We begin with a comprehensive discussion of the punctual Hilbert scheme of the regular two-dimensional local ring in terms of the Gr\"obner cells. These schemes are the most degenerate fibers of the Grothendieck-Deligne norm map (the…

Let f be a dominant meromorphic self-map on a compact Kaehler manifold X which preserves a fibration given by a meromorphic map from X to a compact Kaehler manifold Y. We compute the dynamical degrees of f in term of its dynamical degrees…

A fibration of graphs is an homomorphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. Recently, it has been shown that graph fibrations are useful…

We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

It is proved that a general Fano hypersurface of index 1 (in the projective space) with isolated singularities of general position is birationally rigid. Therefore it cannot be fibered into uniruled varieties of a smaller dimension by a…

In 2002, Biss investigated on a kind of fibration which is called rigid covering fibration (we rename it by rigid fibration) with properties similar to covering spaces. In this paper, we obtain a relation between arbitrary topological…

In this paper we study boundedness properties and singularities of log Calabi-Yau fibrations, particularly those admitting Fano type structures. A log Calabi-Yau fibration roughly consists of a pair $(X,B)$ with good singularities and a…

We prove that any planar birational integrable map, which preserves a fibration given by genus $0$ curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics…

Let $G$ be a topological group and let $K,L\subseteq G$ be closed subgroups, with $K\subseteq L$. We prove that if $L$ is a locally compact pro-Lie group, then the map $q:G/K\to G/L$ is a fibration. As an application of this, we obtain two…

Finitely many hypersurfaces are removed from unordered configuration spaces of $n$ points in $\mathbb{C}$ to obtain a fibration over unordered configuration spaces of $n-1$ complex points. Fundamental groups of these restricted…

We classify elliptic fibrations birational to a nonsingular, minimal cubic surface over a field of characteristic zero. Our proof is adapted to provide computational techniques for the analysis of such fibrations, and we describe an…

We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of…

We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…

We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (Conner-Herfort-Pavesic:…

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…