Related papers: Finite $\mathcal{A}$-determinacy of generic homoge…

We prove a result that relates the number of homomorphisms from the fundamental group of a compact nonorientable surface to a finite group $G$, where conjugacy classes of the boundary components of the surface must map to prescribed…

Let $F:(\mathbb{C}^2,0)\to (\mathbb{C}^n,0)$ be the germ of a finite map and $(X,0)$ be its image. We will in this article using the topology of the link show that $(X,0)$ has to be a quotient singularity if it is normal and describe the…

Let $\mathscr{C}$ be a symmetric tensor category of moderate growth, and let $\mathcal{H}\subseteq\mathcal{G}$ be algebraic groups in $\mathscr{C}$. We prove that the homogeneous space $\mathcal{G}/\mathcal{H}$ exists and is of finite type…

A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a…

Let $C$ be a nonsingular projective curve over an algebraically closed field of characteristic $p>0$ and $I\subset C$ be a finite set. If $\mathcal{U}_{C,\,\omega}$ denotes the moduli space of semistable parabolic bundles of rank $r$ and…

Let $f$ be a homogeneous polynomial of even degree $d$. We study the decompositions $f=\sum_{i=1}^r f_i^2$ where $\mathrm{deg} f_i=d/2$. The minimal number of summands $r$ is called the $2$-rank of $f$, so that the polynomials having…

Let $F(z)=\mathcal{R}e(P(z)) + h.o.t$ be such that $M=(F=0)$ defines a germ of real analytic Levi-flat at $0\in\mathbb{C}^{n}$, $n\geq{2}$, where $P(z)$ is a homogeneous polynomial of degree $k$ with an isolated singularity at…

We determine all affinely homogeneous hypersurfaces S^3 in R^4 whose Hessian is (invariantly) of constant rank 2, including the simply transitive ones. We find 34 inequivalent terminal branches yielding each to a nonempty moduli space of…

We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full…

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the…

Let $G$ be a connected, simply connected, simple, complex, linear algebraic group. Let $P$ be an arbitrary parabolic subgroup of $G$. Let $X=G/P$ be the $G$-homogeneous projective space attached to this situation. Let $d\in H_2(X)$ be a…

Let $C$ be a complex affine reduced curve, and denote by $H^1(C)$ its first truncated cohomology group, i.e. the quotient of all regular differential 1-forms by exact 1-forms. First we introduce a nonnegative invariant $\mu'(C,x)$ that…

In the paper, we first classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in the case that $JH$ is nilpotent and $\deg_zv\leq 1$. After that, we generalize the structure of $H$ to…

In this paper, we study the relation between two dynamical systems (V,f) and (V,g) with f. g = g . f. As an application, we show that an endomorphism (respectively a polynomial map with Zariski dense, of bounded Pre(f) has only finitely…

Let N and P be smooth manifolds of dimensions n and p (n \geq p \geq 2) respectively. Let \Omega(N,P) denote an open subspace of J^{infty}(N,P) which consists of all regular jets and jets with prescribed singularities of types A_{i}, D_{j}…

We show that for all homogeneous polynomials $ f_{m}$ of degree $m$, in $d$ variables, and each $j = 1, \dots , d$, we have \begin{equation*} \left\langle x_{j}^{2}f_{m},f_{m}\right\rangle _{L^{2}\left( \mathbb{S}% ^{d-1}\right) } \geq…

We provide a new way of simultaneously parametrizing arbitrary local CR maps from real-analytic generic manifolds $M\subset {\mathbb C}^N$ into spheres ${\mathbb S}^{2N'-1}\subset {\mathbb C}^{N'}$ of any dimension. The parametrization is…

We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups. The proof uses algebraic self-maps of…

Let $F:\Cn \to \Cn$ be a polynomial mapping in Yagzhev's form,i.e. $$F(x_1,\ld,x_n)=(x_1+H_1(x_1,\ld,x_n),\ld,x_n+H_n(x_1,\ld,x_n)),$$ where $H_i$ are homogenous polynomials of degree 3. In this paper we show that if $\Jac(F) \in…

We study binomial D-modules, which generalize A-hypergeometric systems. We determine explicitly their singular loci and provide three characterizations of their holonomicity. The first of these states that a binomial D-module is holonomic…