Comptes Rendus
no. 5
Ordinary differential equations/Analytic geometry
On the number of fibrations transverse to a rational curve in complex surfaces
[Sur le nombre de fibrations transverses à une courbe rationnelle dans une surface]

Présenté par : Claire Voisin

Maycol Falla Luza1 ; Frank Loray2
1 UFF, Universidad Federal Fluminense, rua Mário Santos Braga S/N, Niterói, RJ, Brazil
2 IRMAR, Université de Rennes-1, 35042 Rennes cedex, France
Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 470-474.

Nous étudions l'existence et le défaut d'unicité de fibrations holomorphes en disques transverses à une courbe rationnelle dans une surface complexe.

We investigate the existence, and lack of uniqueness, of a holomorphic fibration by discs transverse to a rational curve in a complex surface.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.03.002
Maycol Falla Luza 1 ; Frank Loray 2

1 UFF, Universidad Federal Fluminense, rua Mário Santos Braga S/N, Niterói, RJ, Brazil
2 IRMAR, Université de Rennes-1, 35042 Rennes cedex, France 
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Maycol Falla Luza; Frank Loray. On the number of fibrations transverse to a rational curve in complex surfaces. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 470-474. doi : 10.1016/j.crma.2016.03.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.03.002/

[1] M. Falla Luza, F. Loray, Projective connections and neighborhoods of rational lines, in preparation.

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[3] J.C. Hurtubise; N. Kamran Projective connections, double fibrations, and formal neighborhoods of lines, Math. Ann., Volume 292 (1992), pp. 383-409

[4] W. Kryński Webs and projective structures on a plane, Differ. Geom. Appl., Volume 7 (2014), pp. 133-140

[5] S.R. LeBrun Jr., Spaces of complex geodesics and related structures, PhD thesis.

[6] M.B. Mishustin Neighborhoods of the Riemann sphere in complex surfaces, Funct. Anal. Appl., Volume 27 (1993), pp. 176-185

[7] V.I. Savel'ev Zero-type imbedding of a sphere into complex surfaces, Vestn. Mosk. Univ., Ser. I Mat. Mekh., Volume 85 (1982) no. 4, pp. 28-32

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