A constructive proof of the density of algebraic Pfaff equations without algebraic solutions
type: Item
instance of: scholarly article
title: A constructive proof of the density of algebraic Pfaff equations without algebraic solutions
zbMATH Open document ID: 1130.34065
author: Yanyan Li
publication date: 2007-11-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10272
review text: The author presents a constructive proof of Jouanolou's theorem, which was proved by using projective varieties, that the set of algebraic Pfaff equation without algebraic solution over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree. The author also constructs an example of a Pfaff equation with coefficients in the field of Gaussian numbers, that does not have any algebraic solutions. The construction is explicit and can be implemented as an algorithm.
Mathematics Subject Classification ID: 34M45
Mathematics Subject Classification ID: 11R04
zbMATH DE Number: 5214653
zbMATH Keywords: Pfaff equation
zbMATH Keywords: singularity
zbMATH Keywords: algebraic solution
reviewed by: Yuefei Wang
MaRDI profile type: Publication
OpenAlex ID: W2465389672
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DOI: 10.5802/AIF.2308
published in: Annales de l’institut Fourier
description: scientific article