An Algebraic Analysis of Conchoids to Algebraic Curves

Sendra Pons, J. Rafael y Sendra Pons, Juana (2008). An Algebraic Analysis of Conchoids to Algebraic Curves. "Applicable Algebra in Engineering Communication and Computing", v. 19 (n. 5); pp. 413-428. ISSN 0938-1279. https://doi.org/10.1007/s00200-008-0081-1.

Descripción

Título: An Algebraic Analysis of Conchoids to Algebraic Curves
Autor/es:
  • Sendra Pons, J. Rafael
  • Sendra Pons, Juana
Tipo de Documento: Artículo
Título de Revista/Publicación: Applicable Algebra in Engineering Communication and Computing
Fecha: Octubre 2008
Volumen: 19
Materias:
Palabras Clave Informales: Algebraic Curves, analysis, curve C.
Escuela: E.U.I.T. Telecomunicación (UPM) [antigua denominación]
Departamento: Matemática Aplicada a la Ingeniería Técnica de Telecomunicación [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

We study the conchoid to an algebraic affine plane curve C from the perspective of algebraic geometry, analyzing their main algebraic properties. Beside C, the notion of conchoid involves a point A in the affine plane (the focus) and a nonzero field element d (the distance).We introduce the formal definition of conchoid by means of incidence diagrams.We prove that the conchoid is a 1-dimensional algebraic set having atmost two irreducible components. Moreover, with the exception of circles centered at the focus A and taking d as its radius, all components of the corresponding conchoid have dimension 1. In addition, we introduce the notions of special and simple components of a conchoid. Furthermore we state that, with the exception of lines passing through A, the conchoid always has at least one simple component and that, for almost every distance, all the components of the conchoid are simple. We state that, in the reducible case, simple conchoid components are birationally equivalent to C, and we show how special components can be used to decide whether a given algebraic curve is the conchoid of another curve.

Más información

ID de Registro: 2948
Identificador DC: http://oa.upm.es/2948/
Identificador OAI: oai:oa.upm.es:2948
Identificador DOI: 10.1007/s00200-008-0081-1
URL Oficial: http://www.springerlink.com/content/100499/
Depositado por: Memoria Investigacion
Depositado el: 03 May 2010 12:35
Ultima Modificación: 20 Abr 2016 12:33
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