arXiv subjects

Cezar Joiţa

Publications and source records attributed to Cezar Joiţa.

11 recordsLinked to original sources

arXiv2025

Euclidean distance discriminants and Morse attractors

Our study concerns the Euclidean distance function in case of complex plane curves. We decompose the ED discriminant into components which are responsible for three types of behavior of the Morse points. Besides the traditional focal component, which is non--linear; the other components are lines. In particular we shed light on the ``atypical discriminant'' which is due to the loss of Morse critical points at isotropic points at infinity. This phenomenon is specific for the complex setting. We find formulas for the number of Morse singularities which abut to the corresponding type of attractors when moving the centre of the distance function toward a point of the discriminant.

math.AG↗

arXiv2025

Bifurcations of polynomial maps with diffeomorphic and connected fibers

We show the existence of polynomial maps which have a regular bifurcation value, while over a neighbourhood of this value the fibres are connected and diffeomorphic.

math.AG↗

arXiv2025

Tame deformations of highly singular function germs

We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy.

math.AG↗

arXiv2024

Deformations with fibre constancy

For studying the local topology of maps, one uses deformations which split the singularities into simpler ones while preserving the general fibres. We give conditions under which such conservation holds.

math.AG↗

arXiv2024

The image complexity of an analytic map germ

The image of a holomorphic map germ is not necessarily locally open, and it is not always well-defined as a set germ. We find the structure of what becomes the image of a map germ when the target is a surface. We encode it as a decorated tree and we derive a complexity degree.

math.CV↗

arXiv2023

Fibrations of tamely composable maps

We study composed map germs with respect to their local fibrations. Under most general conditions, inspired by the tameness condition that was introduced recently, we prove the existence of singular tube fibrations, and we determine the topology of the fibres.

math.AG↗

arXiv2021

The local image problem for complex analytic maps

We address the question "when the local image of a map is well defined" and answer it in case of holomorphic map germs with target $(\bC^{2}, 0)$. We prove a criterion for holomorphic map germs $(X, x)\to (Y, y)$ to be locally open, solving a conjecture by Huckleberry in all dimensions.

math.CV↗

arXiv2020

Atypical points at infinity and algorithmic detection of the bifurcation locus of real polynomials

We show that the variation of the topology at infinity of a two-variable polynomial function is localisable at a finite number of "atypical points" at infinity. We construct an effective algorithm with low complexity in order to detect sharply the bifurcation values of the polynomial function.

math.AG↗

arXiv2019

Images of analytic map germs, and singular fibrations

For a map germ $G$ with target $(\mathbb C^{p}, 0)$ or $(\mathbb R^{p}, 0)$ with $p\ge 2$, we address two phenomena which do not occur when $p=1$: the image of $G$ may be not well-defined as a set germ, and a local fibration near the origin may not exist. We show how these two phenomena are related, and how they can be characterised.

math.CV↗

arXiv2011

Convexity properties of coverings of 1-convex surfaces

We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.

math.CV↗

arXiv2005

On a Problem of Bremermann Concerning Runge Domains

We give an example of a bounded Stein domain in $\mathbb{C}^n$, with smooth boundary, which is not Runge and whose intersection with every complex line is simply connected.

math.CV↗