A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions

Coutinho, S. C.

doi:10.5802/aif.2308

A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions
[Une preuve constructive de la densité des équations de Pfaff sans solutions algébriques]

Coutinho, S. C.^1,²

¹ Universidade Federal do Rio de Janeiro Departamento de Ciência da Computação Instituto de Matemática P.O. Box 68530, 21945-970 Rio de Janeiro, RJ (Brazil)
² Programa de Engenharia de Sistemas e Computação COPPE, UFRJ, PO Box 68511 21941-972, Rio de Janeiro, RJ (Brazil)

Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1611-1621.

Résumé
Abstract

Nous présentons une preuve constructive du fait que l’ensemble des équations de Pfaff sans solutions algébriques sur le plan projectif complexe est dense dans l’ensemble de toutes les équations algébriques de Pfaff d’un degré donné.

We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.

MR Zbl

DOI : 10.5802/aif.2308

Classification : 11R04, 37F75, 34M45, 32S65
Keywords: Pfaff equation, singularity, algebraic solution
Mot clés : équations de Pfaff, singularité, solution algébrique

Affiliations des auteurs :

Coutinho, S. C. ^{1, 2}

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     author = {Coutinho, S. C.},
     title = {A constructive proof of the {Density} {of~Algebraic} {Pfaff} {Equations} without {Algebraic} {Solutions}},
     journal = {Annales de l'Institut Fourier},
     pages = {1611--1621},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {57},
     number = {5},
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     doi = {10.5802/aif.2308},
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Coutinho, S. C. A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions. Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1611-1621. doi : 10.5802/aif.2308. http://www.numdam.org/articles/10.5802/aif.2308/

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