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

2018/05/18 by Bisquert, Fuensanta Aroca, Calderón, Angelito Camacho, Morales, Mirna Gómez
#14HXX #14TXX #51N35 #58A05 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.07326

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 ≥ 13, which is the best known up until now.

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