no. 3
Logarithmic foliations
Cerveau, Dominique1 ; Neto, Alcides Lins2
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, Série 6, Tome 30 (2021) no. 3, pp. 561-618.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1685
Classification : 37F75, 32G34, 32S65, 37F75, 34M15
Mots clés : holomorphic foliation, logarithmic form
Cerveau, Dominique 1 ; Neto, Alcides Lins 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 
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Cerveau, Dominique; Neto, Alcides Lins. Logarithmic foliations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 30 (2021) no. 3, pp. 561-618. doi : 10.5802/afst.1685. http://archive.numdam.org/articles/10.5802/afst.1685/

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

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

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

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

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

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

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

[8] Cukierman, Fernando; Pereira, Jorge Vitório; Vainsencher, Israel 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] De Medeiros, Airton S. Singular foliations and differential p-forms, Ann. Fac. Sci. Toulouse, Math., Volume 9 (2000) no. 3, pp. 451-466 | DOI | Numdam | MR | Zbl

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

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

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

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

[14] Hamm, Helmut A. 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] Hirsch, Morris W; Pugh, Charles Chapman; Shub, Michael Invariant manifolds, Lecture Notes in Mathematics, 583, Springer, 1977

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

[18] Lins Neto, Alcides; Costa e Silva, Wancossil 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] Martinet, Jean 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] Milnor, John Singular points of complex hypersurfaces, Princeton University Press, 1968 no. 61 | Zbl

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

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

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

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