Experimental Mathematics

On Holomorphic Foliations Without Algebraic Solutions

S. C. Coutinho and Bruno F. M. Ribeiro

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Abstract

We give a symbolic algorithm to check whether certain holomorphic foliations of the complex projective plane have an algebraic solution. This algorithm is then used to produce new examples of foliations without algebraic solutions.

Article information

Source
Experiment. Math., Volume 10, Number 4 (2001), 529-536.

Dates
First available in Project Euclid: 26 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1069855252

Mathematical Reviews number (MathSciNet)
MR1881753

Zentralblatt MATH identifier
1035.37034

Subjects
Primary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 34A05: Explicit solutions and reductions 34C05: Location of integral curves, singular points, limit cycles
Secondary: 58F18

Keywords
Gröbner bases holomorphic foliation algebraic solution

Citation

Coutinho, S. C.; Ribeiro, Bruno F. M. On Holomorphic Foliations Without Algebraic Solutions. Experiment. Math. 10 (2001), no. 4, 529--536. https://projecteuclid.org/euclid.em/1069855252


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