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.
Keywords: Pfaff equation, singularity, algebraic solution
Mot clés : équations de Pfaff, singularité, solution algébrique
@article{AIF_2007__57_5_1611_0, 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}, year = {2007}, doi = {10.5802/aif.2308}, zbl = {1130.34065}, mrnumber = {2364144}, language = {en}, url = {https://www.numdam.org/articles/10.5802/aif.2308/} }
TY - JOUR AU - Coutinho, S. C. TI - A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions JO - Annales de l'Institut Fourier PY - 2007 SP - 1611 EP - 1621 VL - 57 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://www.numdam.org/articles/10.5802/aif.2308/ DO - 10.5802/aif.2308 LA - en ID - AIF_2007__57_5_1611_0 ER -
%0 Journal Article %A Coutinho, S. C. %T A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions %J Annales de l'Institut Fourier %D 2007 %P 1611-1621 %V 57 %N 5 %I Association des Annales de l’institut Fourier %U https://www.numdam.org/articles/10.5802/aif.2308/ %R 10.5802/aif.2308 %G en %F AIF_2007__57_5_1611_0
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. https://www.numdam.org/articles/10.5802/aif.2308/
[1] Some remarks on indices of holomorphic vector fields, Publ. Mat., Volume 41 (1997) no. 2, pp. 527-544 | EuDML | MR | Zbl
[2] Holomorphic foliations in
[3] On the density of algebraic foliations without algebraic invariant sets, J. Reine Angew. Math., Volume 594 (2006), pp. 117-135 | DOI | MR | Zbl
[4] Algebraic solutions of Holomorphic Foliations: an Algorithmic Approach, Journal of Symbolic Computation, Volume 41 (2006), pp. 603-618 | DOI | MR | Zbl
[5] Using algebraic geometry, Undergraduate Texts in Mathematics, Springer, New York, 1998 | Zbl
[6] Axiom: the thirty year horizon, volume 1: tutorial, Lulu Press, 2005
[7] Mémoire sur les équations différentielles algébriques du I
[8] Equations de Pfaff algébriques, Lect. Notes in Math., 708, Springer-Verlag, Heidelberg, 1979 | MR | Zbl
[9] Algebra, Addison-Wesley, Reading, 1974 | MR | Zbl
[10] Around Jouanolou non-integrability theorem, Indag. Mathem., Volume 11 (2000), pp. 239-254 | DOI | MR | Zbl
[11] Algebraic solutions of polynomial differential equations and foliations in dimension two, Holomorphic Dynamics (Lect. Notes in Math.), Volume 1345, New York-Heidelberg-Berlin (1988), pp. 192-232 | MR | Zbl
[12] On the non-existence of constants of derivations: the proof of a theorem of Jouanolou and its development, Bull. Sci. math., Volume 123 (1995), pp. 195-233 | MR | Zbl
[13] Elementary first integrals of differential equations, Trans. Amer. Math. Soc., Volume 279 (1983) no. 1, pp. 215-229 | DOI | MR | Zbl
- Closed Meromorphic 1-Forms, Handbook of Geometry and Topology of Singularities V: Foliations (2024), p. 447 | DOI:10.1007/978-3-031-52481-3_9
- Existence and Uniqueness Theorems for the Pfaff Equation with Continuous Coefficients, Journal of Mathematical Sciences, Volume 278 (2024) no. 3, p. 385 | DOI:10.1007/s10958-024-06928-1
- An Existence Theorem and an Approximate Solution Method for a Pfaff Equation with Continuous Coefficients, Proceedings of the Steklov Institute of Mathematics, Volume 317 (2022) no. S1, p. S16 | DOI:10.1134/s0081543822030026
- On the construction of holomorphic foliations without invariant subvarieties of positive dimension, Bulletin des Sciences Mathématiques, Volume 140 (2016) no. 8, p. 935 | DOI:10.1016/j.bulsci.2016.07.001
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