相关论文: Fields of CR meromorphic functions

The problem of existence of ground state representations on the CCR algebra with free evolution are discussed and all the solutions are classified in terms of non regular or indefinite invariant functionals. In both cases one meets unusual…

Given a compact set $K$ in the plane, which does not contain any triple of points forming a vertical and a horizontal segment, and a map $f\in C(K)$, we give a construction of functions $g,h\in C(\mathbb R)$ such that $f(x,y)=g(x)+h(y)$ for…

A longstanding and important problem in algebraic geometry is the characterization of algebraic function fields. In this paper, we focus on the characterization problem for cyclotomic function field $L(\Lambda_M)$, which is an important…

Let $\mathbb{K}$ be the algebraic closure of a finite field $\mathbb{F}_q$ of odd characteristic $p$. For a positive integer $m$ prime to $p$, let $F=\mathbb{K}(x,y)$ be the transcendency degree $1$ function field defined by…

We show that a pseudo-holomorphic embedding of an almost-complex $2n$-manifold into almost-complex $(2n + 2)$-Euclidean space exists if and only if there is a CR regular embedding of the $2n$-manifold into complex $(n + 1)$-space. We remark…

Let $K$ be a local field whose residue field has characteristic $p$ and let $L/K$ be a finite separable totally ramified extension of degree $n=up^{\nu}$. Let $\sigma_1,\dots,\sigma_n$ denote the $K$-embeddings of $L$ into a separable…

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…

It is known that, among all the monotone decompositions of a planar compact set K with Peano hyperspaces, there exists a unique one that is finer than all the others. We call it the "core decomposition" of K with Peano hyperspace. The…

The notion of meromorphic convexity is defined and studied on complex manifolds. Using this notion, in analogy with Stein manifolds, a new class of complex manifolds, called {\calligra M }-manifolds, is introduced. This is a class of…

A complex projective manifold is rationally connected, resp. rationally simply connected, if finite subsets are connected by a rational curve, resp. the spaces parameterizing these connecting rational curves are themselves rationally…

Suppose that a function $F$ is meromorphic in the domain $\mathbb H(-m) = \{ z : \mathrm{Im}\, z > -m(\mathrm{Re}\, z) \}$, where $m$ is an even, positive, and continuous function that does not increase on $\mathbb R_{\ge 0}$, and suppose…

It is shown that a real-valued formal meromorphic function on a formal generic submanifold of finite Kohn-Bloom-Graham type is necessarily constant.

A semiholomorphic foliations of type (n, d) is a differentiable real manifold X of dimension 2n + d, foliated by complex leaves of complex dimension n. In the present work, we introduce an appropriate notion of pseudoconvexity (and…

Let $k_1,k_2$ be two fields of characteristic 0. Let $G_1$ be a split semisimple algebraic group over $k_1$, $G_2$ a split Kac--Moody group over $k_2$ and $\phi\colon G_1(k_1)\to G_2(k_2)$ an abstract embedding. We show that $\im \phi$ is a…

Let $(A,\mathfrak{m})$ be a hypersurface local ring of dimension $d \geq 1$, $N$ a perfect $A$-module and let $I$ be an ideal in $A$ with $\ell(N/IN)$ finite. We show that there is a integer $r_I \geq -1$ (depending only on $I$ and $N$)…

It follows from the 2004 work of the first author, X.Huang, and D. Zaitsev that any local CR embedding $f$ of a strictly psedoconvex hypersurface $M^{2n+1}\subset\bC^{n+1}$ into the sphere $\bS^{2N+1}\subset \bC^{N+1}$ is rigid, i.e.\ any…

In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…

We prove that generic homologically nontrivial $(2n-1)$-parameter family of analytic discs attached by their boundaries to a CR manifold $\Omega$ in $\mathbb C^n, n \le 2$ tests CR functions: if a smooth function on $\Omega$ extends…

For a cubic rational function with coefficients in a non-archimedean field $K$ whose residue characteristic is $0$ or greater than $3$, there are $2$ possibilities for the shape of its Berkovich ramification locus, considered as an…

We investigate the manifold $\cal{M}$ of (real) quadratic forms in n > 1 variables having a multiple eigenvalue. In addition to known facts, we prove that 1) $\cal{M}$ is irreducible, 2) in the case of n = 3, scalar matrices and only them…