Related papers: Irreducible holonomy groups and Riccati foliations…

Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in…

The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy being that this should force the group to be, in some sense,…

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more…

We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper (1983); the same holds in the singular cases of Bigonnet and Pradines (1985) and…

It is proven that the identity component of the group preserving the leaves of a generalized foliation is perfect. This shows that a well-known simplicity theorem on the diffeomorphism group extends to the nontransitive case.

We study analytic integrable deformations of the germ of a holomorphic foliation given by $df=0$ at the origin $0 \in \mathbb C^n, n \geq 3$. We consider the case where $f$ is a germ of an irreducible and reduced holomorphic function. Our…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

In the current article we study complex cycles of higher multiplicity in a specific polynomial family of holomorphic foliations in the complex plane. The family in question is a perturbation of an exact polynomial one-form giving rise to a…

The article examines a set of irreducible germs $f_P:U_P\to V_p$ of %finite generic morphisms $f:S\to\mathbb P^2$ to the projective plane whose branch curve germs $B_P\subset V_p$ have singularities equisingular deformation equivalent to…

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy…

We study those real $\mathcal{C}^\infty$ foliations in complex surfaces whose leaves are holomorphic curves. The main motivation is to try and understand these foliations in neighborhoods of curves: can we expect the space of foliations in…

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…

The main goal of this paper is the analytic classification of the germs of singular foliations generated, up to an analytic change of coordinates, by the germs of vector fields of form the…

We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…

Let $G$ be a finitely generated group that can be written as an extension \[ 1 \longrightarrow K \stackrel{i}{\longrightarrow} G \stackrel{f}{\longrightarrow} \Gamma \longrightarrow 1 \] where $K$ is a finitely generated group. By a study…

We say that the the germ of a singular holomorphic foliation on $(\mathbb{C}^2,0)$ is algebraizable whenever it is holomorphically conjugate to the singularity of a foliation defined globally on a projective algebraic surface. The object of…

We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries and the group of symmetries are not finite, in contrast with…

Let $\Gamma$ be a group acting on a scheme $X$ and on a Lie superalgebra $\mathfrak{g}$, both defined over an algebraically closed field of characteristic zero $\Bbbk$. The corresponding equivariant map superalgebra $M(\mathfrak{g},…