On the special parabolic points and the topology of the parabolic curve of certain smooth surfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℝ</mml:mi> <mml:mn>3</mml:mn> </mml:msup></mml:math>

Ortiz-Rodríguez, Adriana

doi:10.1016/s1631-073x(02)02287-2

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Cited by 3 publications

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“…We also know of no general techniques for constructing hessian curves with a prescribed configuration. One of us (Ortiz-Rodríguez) investigated this question [4,5] and constructed polynomials f ∈ R[x, y] of degree n whose hessians had n−1 2 ovals in R 2 . When n is 4, 5, and 6, these numbers are 3, 6, and 10, respectively.…”

Section: Introductionmentioning

confidence: 99%

On some combinatorial formulae coming from Hessian Topology

Ortiz-Rodríguez¹,

Sánchez-Bringas

2019

Discrete Mathematics

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The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a topological property of certain spaces whose elements are graphs of a class of hyperbolic polynomials. These identities are proven by different methods in combinatorics.

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Section: Introductionmentioning

confidence: 99%

On some combinatorial formulae coming from Hessian Topology

Ortiz-Rodríguez¹,

Sánchez-Bringas

2019

Discrete Mathematics

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

Aroca

Calderón

Gómez-Morales

2020

RACSAM

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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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Quelques aspects sur la géométrie des surfaces algébriques réelles

Ortiz-Rodríguez

2003

Bulletin des Sciences Mathématiques

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On the special parabolic points and the topology of the parabolic curve of certain smooth surfaces in ℝ 3

Cited by 3 publications

References 7 publications

On some combinatorial formulae coming from Hessian Topology

On some combinatorial formulae coming from Hessian Topology

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

Quelques aspects sur la géométrie des surfaces algébriques réelles

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