J. Nuño-Ballesteros

activity

20142025

most citedSingularities of mappings on ICIS and applications to Whitney equisingularity

3 citations · 8 across the 14 of their papers we have counts for

collaborators

16 papers

math.AG2025

On the topology of complex map-germs and a general Lê-Greuel formula

Lê Dũng Tráng, Juan J. Nuño-Ballesteros, José Seade

Consider a singular holomorphic map-germ $f : (X, 0) \to (C, 0)$ where $X$ is a singular complex analytic variety in $C^{N}$ , and another holomorphic map-ger…

math.AG2025

Counting $D_{4}$ singularities in the image of a wave front

C. Muñoz-Cabello, J. J. Nuño-Ballesteros, R. Oset Sinha

We give a formula to count the number of $D_{4}$ singularities in a stable frontal perturbation of a corank $2$ wave front singularity $f : (C^{3}, 0) \to (C^{4}, 0)$ …

math.AG2024

The Bruce-Roberts Numbers of 1-Forms on an ICIS

Bárbara K. Lima-Pereira, Juan José Nuño-Ballesteros, Bruna Oréfice-Okamoto +1

We relate the Bruce-Roberts numbers of a 1-form with respect to an ICIS to other invariants as the GSV-index, Tjurina and Milnor numbers.

math.AG2023

Disentangling mappings defined on ICIS

Alberto Fernández-Hernández, Juan J. Nuño-Ballesteros

We study germs of hypersurfaces $(Y, 0) \subset (C^{n + 1}, 0)$ that can be described as the image of $A$ -finite mappings $f : (X, S) \to (C^{n + 1}, 0)$ defin…

math.AG2023

On invariants of a map germ from n-space to 2n-space

Juan José Nuño-Ballesteros, Otoniel Nogueira da Silva, João Nivaldo Tomazella

We consider $A$ -finite map germs $f$ from $(C^{n}, 0)$ to $(C^{2 n}, 0)$ . First, we show that the number of double points that appears in a stabilization of…

math.AG2022

The Bruce-Roberts Numbers of a Function on an ICIS

Bárbara K. Lima-Pereira, Juan José Nuño-Ballesteros, Bruna Oréfice-Okamoto +1

We give formulas for the Bruce-Roberts number $μ_{B R} (f, X)$ and its relative version $μ_{B R}^{-} (f, X)$ of a function $f$ with respect to an ICIS $(X, 0)$ . We show that $μ_{BR}^{-}(f…

math.AG2021★ 3 cited

Singularities of mappings on ICIS and applications to Whitney equisingularity

R. Giménez Conejero, J. J. Nuño-Ballesteros

We study germs of analytic maps $f : (X, S) \to (C^{p}, 0)$ , when $X$ is an ICIS of dimension $n < p$ . We define an image Milnor number, generalizing Mond's definition, $μ_I…

math.AG2021

The relative Bruce-Roberts number of a function on a hypersurface

Barbara K. Lima-Pereira, Juan Jose Nuno-Ballesteros, Bruna Orefice-Okamoto +1

We consider the relative Bruce-Roberts number $μ_{B R}^{-} (f, X)$ of a function on an isolated hypersurface singularity $(X, 0)$ . We show that $μ_{B R}^{-} (f, X)$ is equal to the sum of…

math.AG2021★ 1 cited

Families of ICIS with constant total Milnor number

Rafaela Soares de Carvalho, Juan José Nuño-Ballesteros, Bruna Oréfice-Okamoto +1

We show that a family of isolated complete intersection singularities (ICIS) with constant total Milnor number has no coalescence of singularities. This extends a well known result…

math.AG2021

Thom condition and Monodromy

R. Giménez Conejero, Lê Dũng Tráng, J. J. Nuño-Ballesteros

We give the definition of the Thom condition and we show that given any germ of complex analytic function $f : (X, x) \to (C, 0)$ on a complex analytic space $X$ , there exists a…

math.AG2020

Equisingularity of families of functions on isolated determinantal singularities

Rafaela S. Carvalho, Juan J. Nuño-Ballesteros, Bruna Oréfice-Okamoto +1

We study the equisingularity of a family of function germs ${f_{t} : (X_{t}, 0) \to (C, 0)}$ , where $(X_{t}, 0)$ are $d$ -dimensional isolated determinantal singularities. We de…

math.AG2020★ 1 cited

The image Milnor number and excellent unfoldings

R. Giménez Conejero, J. J. Nuño-Ballesteros

We show three basic properties on the image Milnor number $μ_{I} (f)$ of a germ $f : (C^{n}, S) \to (C^{n + 1}, 0)$ with isolated instability. First, we show th…

math.AG2019

The Bruce-Roberts number of a function on a hypersurface with isolated singularity

Juan J. Nuño-Ballesteros, Bruna Oréfice-Okamoto, Bárbara K. L. Pereira +1

Let $(X, 0)$ be an isolated hypersurface singularity defined by $ϕ : (C^{n}, 0) \to (C, 0)$ and $f : (C^{n}, 0) \to C$ such that the Bruce-Roberts number…

math.AG2016

A Lê-Greuel type formula for the image Milnor number

J. J. Nuño-Ballesteros, I. Pallarés-Torres

Let $f : (C^{n}, 0) \to (C^{n + 1}, 0)$ be a corank 1 finitely determined map germ. For a generic linear form $p : (C^{n + 1}, 0) \to (C, 0)$ we denote b…

math.AG2016★ 1 cited

A Jacobian module for disentanglements and applications to Mond's conjecture

J. Fernández de Bobadilla, J. J. Nuño-Ballesteros, G. Peñafort-Sanchis

Given a germ of holomorphic map $f$ from $C^{n}$ to $C^{n + 1}$ , we define a module $M (f)$ whose dimension over $C$ is an upper bound for the $A$ -codim…

math.AG2014★ 2 cited

Equisingularity of families of isolated determinantal singularities

J. J. Nuño-Ballesteros, B. Oréfice-Okamoto, J. N. Tomazella

We study the topological triviality and the Whitney equisingularity of a family of isolated determinantal singularities. On one hand, we give a Lê-Ramanujam type theorem for this k…