arXiv subjects

Jorge Mozo-Fernández

Publications and source records attributed to Jorge Mozo-Fernández.

9 recordsLinked to original sources

arXiv2026

Projective Foliations with a Unique Singular Point and Maximum Algebraic Multiplicity

The study of codimension-one holomorphic foliations on the projective plane $\mathbb{CP}^{2}$ with a unique singular point has attracted increasing interest because of its connections with several important problems. In this paper, we focus on holomorphic foliations of degree $d$ having a singular point of maximal multiplicity $d$. We describe explicitly the foliations in this class and characterize those having a unique singular point. We also state some results concerning Hilbert-Mumford stability for these foliations.

math.AG↗

arXiv2024

Remarks on foliations on $\mathbb{CP}^2$ with a unique singular point

This paper is a contribution to the study of foliations on $\mathbb{CP}^2$ with a unique singularity. We provide an explicit example in degree 7 of such a foliation, in the non dicritical case, having a divergent separatrix, and subsequently, we study different families of such foliations in low degree.

math.DS↗

arXiv2019

Tauberian theorems for $k$--summability with respect to an analytic germ

The goal of this article is to establish tauberian theorems for the $k$--summability processes defined by germs of analytic functions in several complex variables. The proofs are based on the tauberian theorems for $k$--summability in one variable and in monomials, and a method of monomialization of germs of analytic functions.

math.CV↗

arXiv2017

Asymptotic expansions and summability with respect to an analytic germ

In a previous article of the authors with M. Canalis-Durand, monomial asymptotic expansions, Gevrey asymptotic expansions and monomial summability were introduced and applied to certain systems of singularly perturbed differential equations. In the present work, we extend this concept, introducing (Gevrey) asymptotic expansions and summability with respect to a germ of an analytic function in several variables - this includes polynomials. The reduction theory of singularities of curves and monomialization of germs of analytic functions are crucial to establish properties of the new notions, for example a generalization of the Ramis-Sibuya theorem for the existence of Gevrey asymptotic expansions. Two examples of singular differential equations are presented for which the formal solutions are shown to be summable with respect to a polynomial: one ordinary and one partial differential equation.

math.CV↗

arXiv2016

An extension of Borel-Laplace methods and monomial summability

In this paper we will show that monomial summability can be characterized using Borel-Laplace like integral transformations depending of a parameter $0<s<1$. We will apply this result to prove 1-summability in a monomial of formal solutions of a family of partial differential equations.

math.CV↗

arXiv2016

Analytic classification of a class of cuspidal foliations in $({\mathbb C}^3,0)$

In this article we study the analytic classification of certain types of quasi-homogeneous cuspidal holomorphic foliations in $(\CC^3,{\bf 0})$ via the essential holonomy defined over one of the components of the exceptional divisor that appears in the reduction of the singularities of the foliation.

math.DS↗

arXiv2016

Tauberian properties for monomial summability with applications to Pfaffian systems

In this paper we will show that monomial summability processes with respect to different monomials are not compatible, except in the (trivial) case of a convergent series. We will apply this fact to the study of solutions of Pfaffian systems with normal crossings, focusing in the implications of the complete integrability condition on these systems.

math.CA↗

arXiv2013

On codimension one foliations with prescribed cuspidal separatrix

In this paper, we will construct a pre-normal form for germs of codimension one holomorphic foliation having a particular type of separatrix, of cuspidal type. We will also give a sufficient condition, in the quasi-homogeneous, three-dimensional case, for these foliations to be of generalized surface type.

math.DS↗

arXiv2011

Strong asymptotic expansions in a multidirection

In this paper we prove that, for asymptotically bounded holomorphic functions defined in a polysector in ${\mathbb C}^n$, the existence of a strong asymptotic expansion in Majima's sense following a single multidirection towards the vertex entails (global) asymptotic expansion in the whole polysector. Moreover, we specialize this result for Gevrey strong asymptotic expansions. This is a generalization of a result proved by A. Fruchard and C. Zhang for asymptotic expansions in one variable, but the proof, mainly in the Gevrey case, involves different techniques of a functional-analytic nature.

math.CV↗