arXiv subjects

Angelito Camacho Calderón

Publications and source records attributed to Angelito Camacho Calderón.

2 recordsLinked to original sources

arXiv2018

Transversal special parabolic points in the graph of a polynomial obtained under Viro's patchworking

In this article we focus on the study of special parabolic points in surfaces arising as graphs of polynomials, we give a theorem of Viro's patchworking type to build families of real polynomials in two variables with a prescribed number of special parabolic points in their graphs. We use this result to build a family of degree d real polynomials in two variables with $(d-4)(2d-9)$ special parabolic points in its graph. This brings the number of special parabolic points closer to the upper bound of $(d-2)(5d-12)$ when $d \geq 13$, which is the best known up until now.

math.AG↗

arXiv2013

On the realization problem of plane real algebraic curves as Hessian curves

The Hessian Topology is a subject having interesting relations with several areas, for instance, differential geometry, implicit differential equations, analysis and singularity theory. In this article we study the problem of realization of a real plane curve as the Hessian curve of a smooth function. The plane curves we consider are constituted either by only outer ovals or inner ovals. We prove that some of such curves are realizable as Hessian curves.

math.DG↗