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

Falla Luza, Maycol1 ; Loray, Frank2
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, Tome 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
Falla Luza, Maycol 1 ; Loray, Frank 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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Falla Luza, Maycol; Loray, Frank. On the number of fibrations transverse to a rational curve in complex surfaces. Comptes Rendus. Mathématique, Tome 354 (2016) no. 5, pp. 470-474. doi : 10.1016/j.crma.2016.03.002. http://www.numdam.org/articles/10.1016/j.crma.2016.03.002/

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

[2] Grauert, H. Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann., Volume 146 (1962), pp. 331-368

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

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

[7] Savel'ev, V.I. 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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