Related papers: Classification of absolutely dicritical foliations…

In this article, we present a complete classification, with normal forms, of the real algebraic curves under blow-spherical homeomorphisms at infinity.

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…

Let G a group of germs of analytic diffeomorphisms in (C^2,0). We find some remarkable properties supposing that G is finite, linearizable, abelian nilpotent and solvable. In particular, if the group is abelian and has a generic dicritic…

In this paper we study bilipschitz equivalences of germs of holomorphic foliations in $(\mathbb{C}^2,0)$. We prove that the algebraic multiplicity of a singularity is invariant by such equivalences. Moreover, for a large class of…

We characterize plane curve germes non-degenerate in Kouchnirenko's sense in terms of characteristics and intersection multiplicities of branches.

We focus on topological equisingularity of families of holomorphic function germs with 1-dimensional critical set. We introduce the notion of equisingularity at the critical set and prove that any family which is equisingular at the…

The singularity space consists of all germs $(X,x)$, with $X$ a Noetherian scheme and $x$ a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a Polish space for the metric given…

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 groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance…

In this paper, we study nilpotent holomorphic foliations in complex dimension $n+1$, at the origin, defined by germs of integrable 1-forms whose linear part is given by \(zdz\). These foliations generalize the classical nilpotent foliations…

In this work we give a complete description of the collection of curves of tangencies induced by germs of foliation pairs -- non dicritical and dicritical -- given by analytic differential equations with degenerated non dicritical and…

A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the…

We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived…

In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure…

We obtain a classification of codimension one holomorphic foliations on $\mathbb P^4$ with degenerate Gauss maps.

A characteristic class for deformations of foliations called the Fuks-Lodder-Kotschick class (FLK class for short) is studied. It seems unknown if there is a real foliation with non-trivial FLK class. In this article, we show some…

We show that on any Riemann surface S of genus g>1 any nonsingular even spin bundle defines e-foloation of S. When a surface is hyperelliptic then all leaves of this foliation are finite and almost all of them consists of 2g+2 points.…

Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for…

It is known that there is at least an invariant analytic curve passing through each of the components in the complement of nodal singularities, after the reduction of singularities of a germ of singular foliation in ${\mathbb C}^2,0$}.…

We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus, generalising recent work of Borodzik and Livingston. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux…