English

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

Algebraic Geometry 2018-05-21 v1 Differential Geometry

Abstract

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 (d4)(2d9)(d-4)(2d-9) special parabolic points in its graph. This brings the number of special parabolic points closer to the upper bound of (d2)(5d12)(d-2)(5d-12) when d13d \geq 13, which is the best known up until now.

Keywords

Cite

@article{arxiv.1805.07326,
  title  = {Transversal special parabolic points in the graph of a polynomial obtained under Viro's patchworking},
  author = {Fuensanta Aroca Bisquert and Angelito Camacho Calderón and Mirna Gómez Morales},
  journal= {arXiv preprint arXiv:1805.07326},
  year   = {2018}
}

Comments

20 pages, 4 figures