Related papers: Monodromy of stratified braid groups, II

We say that a monic polynomial $f(x)\in {\mathbb Z}[x]$ of degree $N\ge 2$ is monogenic if $f(x)$ is irreducible over ${\mathbb Q}$ and $\{1,\theta,\theta^2,\ldots ,\theta^{N-1}\}$ is a basis for the ring of integers of ${\mathbb…

In this paper we construct effective invariants for braid monodromy of affine curves. We also prove that, for some curves, braid monodromy determines their topology. We apply this result to find a pair of curves with conjugate equations in…

We study the arithmetic and geometric iterated monodromy groups associated to the postcritically finite (PCF) quadratic rational function $f(x)=\frac{2}{(x-1)^2}$ defined over a number field $k$, whose critical points are both strictly…

We define a monodromy homomorphism for irreducible families of regular elliptic fibrations which takes values in the mapping class group of a punctured sphere. We compute the monodromy for elliptic fibrations only which contain no singular…

We consider real monic {\em hyperbolic} polynomials in one real variable, i.e. polynomials having only real roots. Call {\em hyperbolicity domain} $\Pi$ of the family of polynomials $P(x,a)=x^n+a_1x^{n-1}+... +a_n$, $a_i,x\in {\bf R}$, the…

In this paper, we consider the family of monic polynomials with prime coefficients and the family of all polynomials with prime coefficients. We determine the number of $f(x)$ in each of these families having: squarefree discriminant;…

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of…

It has been shown recently that monomial maps in a large class respecting the action of the infinite symmetric group have, up to symmetry, finitely generated kernels. We study the simplest nontrivial family in this class: the maps given by…

We study a wide range of homologically-defined representations of surface braid groups and of mapping class groups of surfaces, including the Lawrence-Bigelow representations of the classical braid groups. These representations naturally…

We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into SL_n(C) under conjugation by a single analytic matrix map. We apply this result to the…

Motivated by a problem in complex dynamics, we examine the block structure of the natural action of monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power…

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold…

The orbifold braid groups of two dimensional orbifolds were defined in [1] (arXiv:math/9907194) to understand certain Artin groups as subgroups of some suitable orbifold braid groups. We studied orbifold braid groups in some more detail in…

Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots,…

The critical loci of a map $f:X\to Y$ between smooth schemes over a field $k$ are the locally closed subschemes $\Sigma^i(f)\subseteq X$ where the differential of $f$ has constant rank. We prove that if $f : X\to \mathbb A^r$ is the general…

In this article we study the extent to which an $n$-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a…

We classify generically transitive actions of semidirect products of an additive and a multiplicative group on the projective plane. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's…

In this paper we study the generalized Clifford algebra defined by Pappacena of a monic (with respect to the first variable) homogeneous polynomial $\Phi(Z,X_1,\dots,X_n)=Z^d-\sum_{k=1}^d f_k(X_1,\dots,X_n) Z^{d-k}$ of degree $d$ in $n+1$…

Unlabeled multigraphs have diverse applications across scientific fields, from transportation and social networks to polymer physics. In particular, multigraphs are essential for studying the relationship between the spatial organization…

In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…