Related papers: Automatic meromorphy in non-archimedean geometry

This note surveys basic topological properties of nonarchimedean analytic spaces, in the sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We also discuss interactions between the topology of nonarchimedean…

Let K be an algebraically closed field of characteristic zero, endowed with a complete nonarchimedean norm. Let X be a K-rigid analytic variety and \Sigma a semianalytic subset of X. Then the closure of \Sigma in X with respect to the…

For any noncompact semisimple real Lie group $G$, we construct a group of affine transformations of its Lie algebra $\mathfrak{g}$ whose linear part is Zariski-dense in $\operatorname{Ad} G$ and which is free, nonabelian and acts properly…

In this note we prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.

Let K be a non archimedean algebraically closed field of characteristic pi complete for its ultrametric absolute value. In a recent paper by Escassut and Yang, polynomial decompositions P(f)=Q(g) for meromorphic functions f, g on K (resp.…

We consider the family of all meromorphic functions $f$ of the form $$ f(z)=\frac{1}{z}+b_0+b_1z+b_2z^2+\cdots $$ analytic and locally univalent in the puncture disk $\mathbb{D}_0:=\{z\in\mathbb{C}:\,0<|z|<1\}$. Our first objective in this…

If $X$ is a rational surface without nonzero holomorphic vector field and $f$ is an automorphism of $X$, we study in several examples the Zariski tangent space of the local deformation space of the pair $(X, f)$.

In this paper we prove the following theorem. Let $f:\mathbb{A}^2\rightarrow \mathbb{A}^2$ be a dominate polynomial endomorphisms defined over an algebraically closed field $k$ of characteristic $0$. If there are no nonconstant rational…

We prove that every non-degenerate toric variety, every homogeneous space of a connected linear algebraic group without non-constant invertible regular functions, and every variety covered by affine spaces admits a surjective morphism from…

We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for…

The aim of this paper is that of discussing Closed Graph Theorems for bornological vector spaces in a way which is accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over $\mathbb{R}$ and…

We prove a rigid analytic analogue of the Artin vanishing theorem. Precisely, we prove (under mild hypotheses) that the geometric etale cohomology of any Zariski-constructible sheaf on any affinoid rigid space $X$ vanishes in all degrees…

The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…

We study the class $\mathcal{M}$ of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in $\mathcal{M}$, with at least one essential singularity, permutes with a non-constant rational…

Let $M$ be an open Riemann surface. We prove that every meromorphic function on $M$ is the complex Gauss map of a conformal minimal immersion $M\to\mathbb{R}^3$ which may furthermore be chosen as the real part of a holomorphic null curve…

Let $F$ be a field, let $D$ be a subring of $F$, and let ${\mathfrak{X}}$ be the Zariski-Riemann space of valuation rings containing $D$ and having quotient field $F$. We consider the Zariski, inverse and patch topologies on…

On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A…

Let $(M,g)$ be a simple Riemannian manifold. Under the assumption that the metric $g$ is real-analytic, it is shown that if the geodesic ray transform of a function $f\in L^{2}(M)$ vanishes on an appropriate open set of geodesics, then…

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.

We show that the values of a certain family of weakly holomorphic modular functions at points in the divisors of any meromorphic modular form with algebraic Fourier coefficients are algebraic. We use this to extend the classical result of…