Related papers: On irreducible germs of generic morphisms

We study the relationship between singularities of finite-dimensional integrable systems and singularities of the corresponding spectral curves. For the large class of integrable systems on matrix polynomials, which is a general framework…

Let p be a prime number. We classify all smooth irreducible mod-p representations of the unramified unitary group U(1,1)(Q_p^2/Q_p) in two variables. We then investigate Langlands parameters in characteristic p associated to…

We consider the problem of birationally modifying a morphism of complete varieties to make it a morphism from a nonsingular variety to a normal variety. Our main result is to give a counterexample to this problem. This example also is a…

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.…

We introduce the notion of wide representation of an inverse semigroup and prove that with a suitably defined topology there is a space of germs of such a representation which has the structure of an etale groupoid. This gives an elegant…

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

We study tangential families, i.e. systems of rays emanating tangentially from given curves. We classify, up to Left-Right equivalence, stable singularities of tangential family germs (under deformations among tangential families) and we…

We prove that the preimage of a germ of a singular analytic hypersurface under a germ of a finite holomorphic map $g: (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^n,0)$ is again singular. This provides a generalization of previous results of…

Let $C$ be an irreducible smooth complex projective curve of genus $g$, with $g_C \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$, with $r\geqslant 2$. Let $\mc Q:=\mc Q(E,\,d)$ be the Quot Scheme parameterizing torsion…

We describe, for various degenerations $S\to \Delta$ of quartic $K3$ surfaces over the complex unit disk (e.g., to the union of four general planes, and to a general Kummer surface), the limits as $t\in \Delta^*$ tends to 0 of the Severi…

Let $G$ denote the unramified quasi-split unitary group $\mathbb{U}(1,1)(F)$ over a $p$-adic field $F$ with residual characteristic $p \neq 2$. In this paper, we first construct a large family of irreducible representations of the maximal…

We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singularities appearing in geometric solutions to the equation as well as their duals. We also…

An extremal curve germ is the analytic germ of a threefold with terminal singularities along a reduced complete curve admitting a contraction whose fibers have dimension at most one. The aim of the present paper is to review the results…

We study the notion of irreducibility of semigroup morphisms. Given an alphabet $\Sigma$, a morphism $\varphi:\Sigma^+\rightarrow\Sigma^+$ is irreducible if any factorisation $\varphi=\psi_2\circ\psi_1$ can only be satisfied if $\psi_1$ or…

We classify generic unfoldings of germs of antiholomorphic diffeomorphisms with a parabolic point of codimension 1 (i.e. a double fixed point) under conjugacy. These generic unfolding depend on one real parameter. The classification is done…

A germ of normal complex analytical surface is called a Hirzebruch-Jung singularity if it is analytically isomorphic to the germ at the 0-dimensional orbit of an affine toric surface. Two such germs are known to be isomorphic if and only if…

The SU(2) TQFT representation of the mapping class group of a closed surface of genus g, at a root of unity of prime order, is shown to be irreducible. Some examples of reducible representations are also given.

Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given $cal K$-invariant class in terms of certain stable homotopy groups by applying the…

In this paper we study the problem of analytic extension of germs of holonomy of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is…

In this paper we give a formula for counting the number of isolated stable singularities of a stable perturbation of corank 1 germs $f:\C^n,0\to \C^p,0$ with $n<p$ that appear in the image $f(\C^n).$ We also define a set of ${\cal…