Feuilleter
no. 1
Holomorphic foliations with no transversely projective structure
[Feuilletages holomorphes sans structure projective transverse]
Indranil Biswas1 ; Sorin Dumitrescu2
1Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida, Uttar Pradesh 201314, India
2Université Côte d’Azur, CNRS, LJAD, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 1, pp. 35-56

We prove that on the product of two elliptic curves a generic nonsingular turbulent holomorphic foliation does not admit any transversely holomorphic projective structure.

Nous prouvons que sur le produit de deux courbes elliptiques un feuilletage holomorphe tourbillonné nonsingulier générique n’admet aucune structure projective holomorphe transverse.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1840
Classification : 32M25, 53A20, 53C12
Keywords: Holomorphic foliation, projective structure, transversely projective structure, flat bundle

Indranil Biswas  1   ; Sorin Dumitrescu  2

1 Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida, Uttar Pradesh 201314, India
2 Université Côte d’Azur, CNRS, LJAD, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{AFST_2026_6_35_1_35_0,
     author = {Indranil Biswas and Sorin Dumitrescu},
     title = {Holomorphic foliations with no transversely projective structure},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {35--56},
     year = {2026},
     publisher = {Universit\'e de Toulouse, Toulouse},
     volume = {Ser. 6, 35},
     number = {1},
     doi = {10.5802/afst.1840},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1840/}
}
TY  - JOUR
AU  - Indranil Biswas
AU  - Sorin Dumitrescu
TI  - Holomorphic foliations with no transversely projective structure
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2026
SP  - 35
EP  - 56
VL  - 35
IS  - 1
PB  - Université de Toulouse, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1840/
DO  - 10.5802/afst.1840
LA  - en
ID  - AFST_2026_6_35_1_35_0
ER  - 
%0 Journal Article
%A Indranil Biswas
%A Sorin Dumitrescu
%T Holomorphic foliations with no transversely projective structure
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2026
%P 35-56
%V 35
%N 1
%I Université de Toulouse, Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1840/
%R 10.5802/afst.1840
%G en
%F AFST_2026_6_35_1_35_0
Indranil Biswas; Sorin Dumitrescu. Holomorphic foliations with no transversely projective structure. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 1, pp. 35-56. doi: 10.5802/afst.1840

[1] Michael F. Atiyah Complex analytic connections in fibre bundles, Trans. Am. Math. Soc., Volume 85 (1957), pp. 181-207 | Zbl | DOI

[2] Bruno Azevedo Scárdua Transversely affine and transversely projective holomorphic foliations, Ann. Sci. Éc. Norm. Supér., Volume 30 (1997) no. 2, pp. 169-204 | Zbl | Numdam | MR

[3] Indranil Biswas; Tomás L. Gómez Connections and Higgs fields on a principal bundle, Ann. Global Anal. Geom., Volume 33 (2008) no. 1, pp. 19-46 | Zbl | DOI | MR

[4] Indranil Biswas; Ashok K. Raina Projective structures on a Riemann surface. II, Int. Math. Res. Not., Volume 1999 (1999) no. 13, pp. 685-716 | Zbl | DOI | MR

[5] Marco Brunella Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. Éc. Norm. Supér., Volume 30 (1997) no. 5, pp. 569-594 | Zbl | DOI | Numdam | MR

[6] Marco Brunella Codimension one foliations on complex tori, Ann. Fac. Sci. Toulouse, Math., Volume 19 (2010) no. 2, pp. 405-418 | Zbl | DOI | Numdam

[7] Pierre Deligne Équations différentielles à points singuliers réguliers, Lecture Notes in Mathematics, 163, Springer, 1970, 133 pages | Zbl | DOI

[8] Étienne Ghys Feuilletages holomorphes de codimension un sur les espaces homogènes complexes, Ann. Fac. Sci. Toulouse, Math., Volume 5 (1996) no. 3, pp. 493-519 | Zbl | Numdam | DOI | MR

[9] Alexander Grothendieck Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV, Publ. Math., Inst. Hautes Étud. Sci., Volume 32 (1967), pp. 1-361 (rédigé avec la colloboration de J. Dieudonné) | Numdam | Zbl | MR

[10] Robert C. Gunning Lectures on Riemann Surfaces, Princeton Mathematical Notes, Princeton University Press, 1966 | Zbl | MR

[11] John H. Hubbard The monodromy of projective structures, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (Annals of Mathematics Studies), Volume 97, Princeton University Press, 1978, pp. 257-275 | Zbl

[12] Takashi Inaba; Shigenori Matsumoto Some qualitative aspects of transversely projective foliations, Proc. Japan Acad., Ser. A, Volume 65 (1989) no. 4, pp. 116-118 | Zbl | MR

[13] Federico Lo Bianco; Jorge Vitório Pereira Smooth foliations on homogeneous compact Kähler manifolds, Ann. Fac. Sci. Toulouse, Math., Volume 25 (2016) no. 1, pp. 141-159 | DOI | Numdam | Zbl | MR

[14] Frank Loray; Jorge Vitório Pereira Transversely projective foliations on surfaces: existence of minimal form and prescription of monodromy, Int. J. Math., Volume 18 (2007) no. 6, p. 723-74 | DOI | Zbl | MR

[15] Frank Loray; Jorge Vitório Pereira; Frédéric Touzet Representations of quasi-projective groups, flat connections and transversely projective foliations, J. Éc. Polytech., Math., Volume 3 (2006), pp. 263-308 | Zbl | DOI | MR

[16] Bobo Seke Sur les structures transversalement affines des feuilletages de codimension, Ann. Inst. Fourier, Volume 30 (1980) no. 1, pp. 1-29 | Zbl | Numdam | DOI | MR

Cité par Sources :