arXiv subjects

Juan José Nuño Ballesteros

Publications and source records attributed to Juan José Nuño Ballesteros.

4 recordsLinked to original sources

arXiv2025

Lipschitz geometry of the image of finite mappings

This paper is devoted to the study of the LNE property in complex analytic hypersurface parametrized germs, that is, the sets that are images of finite analytic map germs from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$. We prove that if the multiplicity of $f$ is equal to his generic degree, then the image of $f$ is LNE at 0 if and only if it is a smooth germ. We also show that every finite corank 1 map is sattisfies the previous hypothesis. Moreover, we show that for an injective map germ $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{n+1},0)$, the image of $f$ is LNE at 0 if and only if $f$ is an embedding.

math.AG↗

arXiv2018

Iterated multiple points I: functoriality, defining equations and pathologies

This is the first of a two-part work on Kleiman's iterated multiple point spaces. We show general properties of these spaces, leading to explicit equations describing them for maps (of any corank) between complex manifolds. We also describe pathologies regarding dimension and lack of symmetry

math.AG↗

arXiv2018

Topological Classification and Finite Determinacy of knotted maps

We show that the knot type of the link of a real analytic map germ with isolated singularity $f\colon(\mathbb{R}^2,0)\to(\mathbb{R}^4,0)$ is a complete invariant for $C^0$-$\mathscr A$-equivalence. Moreover, we also prove that isolated instability implies $C^0$-finite determinacy, giving an explicit estimate for its degree. For the general case of real analytic map germs, $f\colon (\mathbb{R}^n,0) \rightarrow (\mathbb{R}^p,0)$ ($n \leq p$), we use the Lojasiewicz exponent associated to the Mond's double point ideal $I^2(f)$ to obtain some criteria of Lipschitz and analytic regularity.

math.AG↗

arXiv2016

Liftable vector fields, unfoldings and augmentations

We study liftable vector fields of smooth map-germs. We show how to obtain the module of liftable vector fields of any map-germ of finite singularity type from the module of liftable vector fields of a stable unfolding of it. As an application, we obtain the liftable vector fields for the family $H_k$ in Mond's list. We then show the relation between the liftable vector fields of a stable germ and its augmentations.

math.CV↗