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arXiv · 1805.07326

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

Fuensanta Aroca Bisquert·Angelito Camacho Calderón·Mirna Gómez Morales
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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 $(d-4)(2d-9)$ 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.

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Fuensanta Aroca Bisquert, Angelito Camacho Calderón, Mirna Gómez Morales. 2018-05-18. Transversal special parabolic points in the graph of a polynomial obtained under Viro's patchworking. https://arxiv.org/abs/1805.07326

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