Transactions of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Liouvillian integration and Bernoulli foliations

Author(s): D. Cerveau; P. Sad
Journal: Trans. Amer. Math. Soc. 350 (1998), 3065-3081.
MSC (1991): Primary 32L30; Secondary 58F18
MathSciNet review: 1390971
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Analytic foliations in the 2-dimensional complex projective space with algebraic invariant curves are studied when the holonomy groups of these curves are solvable. It is shown that such a condition leads to the existence of a Liouville type first integral, and, under ``generic'' extra conditions, it is proven that these foliations can be defined by Bernoulli equations.

References:

1.: C. Camacho, A. Lins Neto and P. Sad, Foliations with Algebraic Limit Sets, Ann. of Math. 136 (1992). MR 93i:32035
2.: C. Camacho and P. Sad, Invariant Varieties Through Singularities of Holomorphic Vector Fields, Ann. of Math. 115 (1982). MR 83m:58062
3.: D. Cerveau and A. Lins Neto, Holomorphic Foliations in $\mathbf{C}P(2)$ having an Invariant Algebraic Curve, Ann. Inst. Fourier 41 (1991). MR 93b:32050
4.: D. Cerveau et J-F. Mattei, Formes Intégrables Holomorphes Singulières, Astérisque 97, Soc. Math. France, 1982. MR 86f:58006
5.: D. Cerveau et R. Moussu, Groupes d'Automorphismes de $(\mathbf{C},0)$ et Équations Différentielles $ydy+\cdots =0$ , Bull. Soc. Math. France. 116 (1988). MR 90m:58192
6.: P. Deligne, Le Groupe Foundamental du Complément d'une Courbe Plane n'ayant que des Points Doubles Ordinaires est Abélian, Sem. Bourbaki, Lecture Notes in Math. 842, Springer, 1981. MR 83f:14026
7.: I. Kaplansky, An Introduction to Differential Algebra, Hermann, Paris, 1957. MR 20:177
8.: A. Lins Neto, Construction of Singular Holomorphic Vector Fields in Dimension Two, J. Differential Geometry 26 (1987). MR 88f:32047
9.: J-F. Mattei et R. Moussu, Holonomie et Intégrales Premières, Ann. Sci. Ecole Norm. Sup. 13 (1980). MR 83b:58005
10.: M. Prelle and M. Singer, Elementary First Integrals of Differential Equations, Trans. Amer. Math. Soc. 279 (1983), 215-229. MR 85d:12008
11.: B. Scárdua, Transversely Affine Foliations on Complex Projective Spaces, IMPA, Thesis.
12.: B. Seke, Sur les Structures Transversalement Affines des Feuilletages de Codimension Un, Ann. Inst. Fourier 30 (1980). MR 82b:57023
13.: M. Singer, Liouvillian First Integrals of Differential Equations, Trans. Amer. Math. Soc. 333 (1992), 673-688. MR 92m:12014
14.: J. Tits, Free Subgroups in Linear Groups, J. Algebra 20 (1972). MR 44:4105

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|