Browse issues
no. 3
Logarithmic foliations
Dominique Cerveau1; Alcides Lins Neto2
1 Inst. Mathématique de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France
2 IMPA, Est. D. Castorina, 110, 22460-320, Rio de Janeiro, RJ, Brazil
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 3, pp. 561-618.

The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.

Nous étudions dans cet article les feuilletages holomorphes singuliers de codimension arbitraire définis par des formes logarithmiques sur les espaces projectifs.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1685
Classification: 37F75, 32G34, 32S65, 37F75, 34M15
Keywords: holomorphic foliation, logarithmic form

Dominique Cerveau 1; Alcides Lins Neto 2

1 Inst. Mathématique de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France
2 IMPA, Est. D. Castorina, 110, 22460-320, Rio de Janeiro, RJ, Brazil
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{AFST_2021_6_30_3_561_0,
     author = {Dominique Cerveau and Alcides Lins Neto},
     title = {Logarithmic foliations},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {561--618},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 30},
     number = {3},
     year = {2021},
     doi = {10.5802/afst.1685},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1685/}
}
TY  - JOUR
AU  - Dominique Cerveau
AU  - Alcides Lins Neto
TI  - Logarithmic foliations
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2021
SP  - 561
EP  - 618
VL  - 30
IS  - 3
PB  - Université Paul Sabatier, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1685/
DO  - 10.5802/afst.1685
LA  - en
ID  - AFST_2021_6_30_3_561_0
ER  - 
%0 Journal Article
%A Dominique Cerveau
%A Alcides Lins Neto
%T Logarithmic foliations
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2021
%P 561-618
%V 30
%N 3
%I Université Paul Sabatier, Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1685/
%R 10.5802/afst.1685
%G en
%F AFST_2021_6_30_3_561_0
Dominique Cerveau; Alcides Lins Neto. Logarithmic foliations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 3, pp. 561-618. doi : 10.5802/afst.1685. https://afst.centre-mersenne.org/articles/10.5802/afst.1685/

[1] Vladimir Igorevich Arnol’d Chapitres supplémentaires de la théorie des équations différentielles ordinaires, Mir, 1980

[2] Wolf Barth Fortsetzung meromorpher Funktionen in Tori und komplex-projektiven Räumen, Invent. Math., Volume 5 (1968) no. 1, pp. 42-62 | DOI | MR | Zbl

[3] Omegar Calvo-Andrade Irreducible components of the space of holomorphic foliations, Math. Ann., Volume 299 (1994) no. 1, pp. 751-767 | DOI | MR | Zbl

[4] César Camacho; Alcides Lins Neto; Paulo Sad Foliations with algebraic limit sets, Ann. Math., Volume 136 (1992) no. 2, pp. 429-446 | DOI | MR | Zbl

[5] Henri Cartan Sur le premier problème de Cousin, C. R. Math. Acad. Sci. Paris, Volume 207 (1938), pp. 558-560 | Zbl

[6] Dominique Cerveau Distributions involutives singulières, Ann. Inst. Fourier, Volume 29 (1979) no. 3, pp. 261-294 | DOI | Numdam | Zbl

[7] Dominique Cerveau; Jean-François Mattei Formes intégrables holomorphes singulières, Astérisque, 97, Société Mathématique de France, 1982 | Numdam | Zbl

[8] Fernando Cukierman; Jorge Vitório Pereira; Israel Vainsencher Stability of foliations induced by rational maps, Ann. Fac. Sci. Toulouse, Math., Volume 18 (2009) no. 4, pp. 685-715 | DOI | Numdam | MR | Zbl

[9] Airton S. De Medeiros Singular foliations and differential p-forms, Ann. Fac. Sci. Toulouse, Math., Volume 9 (2000) no. 3, pp. 451-466 | DOI | Numdam | MR | Zbl

[10] Pierre Deligne Théorie de Hodge II, Publ. Math., Inst. Hautes Étud. Sci., Volume 40 (1971) no. 1, pp. 5-57 | DOI | Numdam | Zbl

[11] Javier Gargiulo Acea Logarithmic forms and singular projective foliations, Ann. Inst. Fourier, Volume 70 (2020) no. 1, pp. 171-203 | DOI | MR | Zbl

[12] Hans Grauert; Reinhold Remmert Theory of Stein spaces, Springer, 1979 | Zbl

[13] Helmut A. Hamm Lokale topologische Eigenschaften komplexer Räume, Math. Ann., Volume 191 (1971) no. 3, pp. 235-252 | DOI | Zbl

[14] Helmut A. Hamm Lefschetz theorems for singular varieties, Singularities, Part 1 (Arcata, Calif., 1981) (Proceedings of Symposia in Pure Mathematics), Volume 40, American Mathematical Society, 1983, pp. 547-557 | MR | Zbl

[15] Morris W Hirsch; Charles Chapman Pugh; Michael Shub Invariant manifolds, Lecture Notes in Mathematics, 583, Springer, 1977

[16] Alcides Lins Neto Componentes Irredutíveis dos Espacos de Folheacões, 2007 26 o Colóquio Brasileiro de Matemática, Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro. Available at: http://www.impa.br/opencms/pt/biblioteca/cbm/26CBM/26CBM02.pdf

[17] Alcides Lins Neto Germs of complex two dimensional foliations, Bull. Braz. Math. Soc. (N.S.), Volume 46 (2015) no. 4, pp. 645-680 | DOI | MR

[18] Alcides Lins Neto; Wancossil Costa e Silva Pull-back components of the space of foliations of codimension≥2, Trans. Am. Math. Soc., Volume 371 (2019) no. 2, pp. 949-969 | MR | Zbl

[19] Jean Martinet Normalisation des champs de vecteurs holomorphes, Séminaire Bourbaki vol. 1980/81 (Lecture Notes in Mathematics), Volume 901, Springer, 1981, pp. 55-70 | DOI | Numdam | MR | Zbl

[20] John Milnor Singular points of complex hypersurfaces, Princeton University Press, 1968 no. 61 | Zbl

[21] Georges de Rham Sur la division de formes et de courants par une forme linéaire, Comment. Math. Helv., Volume 28 (1954) no. 1, pp. 346-352 | Zbl

[22] Hugo Rossi Continuation of subvarieties of projective varieties, Am. J. Math., Volume 91 (1969) no. 2, pp. 565-575 | DOI | MR | Zbl

[23] José Seade On the topology of isolated singularities in analytic spaces, Progress in Mathematics, 241, Birkhäuser, 2006 | MR | Zbl

[24] Yum-Tong Siu Techniques of extension of analytic objects, Lecture Notes in Pure and Applied Mathematics, 8, Marcel Dekker, 1974 | MR | Zbl

Cited by Sources: