On montre l'existence d'un feuilletage holomorphe de dimension un (à singularités isolées non effaçables) sur une surface algébrique affine lisse appropriée de dimension 2 qui est tangent à un champ vectoriel rationnel, et tel qu'aucune famille de feuilles intersectant une section transverse n'admet d'uniformisation holomorphe paramétrée par une famille d'ouverts simplement connexes de
We prove existence of a one-dimensional holomorphic foliation (with isolated irremovable singularities) tangent to a rational vector field on appropriate affine algebraic surface of dimension 2 such that the family of leaves intersecting arbitrary given cross-section does not admit a uniformization holomorphic in the parameter by a family of simply connected domains in
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@article{CRMATH_2002__334_6_489_0, author = {Glutsyuk, Alexey}, title = {On simultaneous uniformization and local nonuniformizability}, journal = {Comptes Rendus. Math\'ematique}, pages = {489--494}, publisher = {Elsevier}, volume = {334}, number = {6}, year = {2002}, doi = {10.1016/S1631-073X(02)02268-9}, language = {en}, url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02268-9/} }
TY - JOUR AU - Glutsyuk, Alexey TI - On simultaneous uniformization and local nonuniformizability JO - Comptes Rendus. Mathématique PY - 2002 SP - 489 EP - 494 VL - 334 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02268-9/ DO - 10.1016/S1631-073X(02)02268-9 LA - en ID - CRMATH_2002__334_6_489_0 ER -
%0 Journal Article %A Glutsyuk, Alexey %T On simultaneous uniformization and local nonuniformizability %J Comptes Rendus. Mathématique %D 2002 %P 489-494 %V 334 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02268-9/ %R 10.1016/S1631-073X(02)02268-9 %G en %F CRMATH_2002__334_6_489_0
Glutsyuk, Alexey. On simultaneous uniformization and local nonuniformizability. Comptes Rendus. Mathématique, Tome 334 (2002) no. 6, pp. 489-494. doi : 10.1016/S1631-073X(02)02268-9. http://www.numdam.org/articles/10.1016/S1631-073X(02)02268-9/
[1] Complete intersections in Stein manifolds, Manuscripta Math., Volume 37 (1982) no. 3, pp. 343-356
[2] Analytic multifunctions, the
[3] Simultaneous uniformization, Bull. Amer. Math. Soc., Volume 66 (1960), pp. 94-97
[4] Nonuniformizable skew cylinders. A counterexample to the simultaneous uniformization problem, C. R. Acad. Sci. Paris, Série I, Volume 332 (2001) no. 3, pp. 209-214
[5] Pseudoholomorphic curves in symplectic manifolds, Invent. Math., Volume 82 (1985) no. 2, pp. 307-347
[6] Foliations by analytic curves, Mat. Sb., Volume 88 (1972) no. 130, pp. 558-577
[7] Nondegenerate B-groups, Soviet Math. Dokl., Volume 14 (1973), pp. 207-210
[8] Covering manifolds for analytic families of leaves of foliations by analytic curves, Topol. Methods Nonlinear Anal., Volume 11 (1998) no. 2, pp. 361-373
[9] Skew cylinders and simultaneous uniformization, Proc. Steklov Inst. Math., Volume 213 (1996), pp. 112-123
[10] Nouvelles recherches sur les fonctions entières de plusieurs variables complexes (II). Fonctions entières qui se reduisent à celles d'une variable, J. Math. Kyoto Univ., Volume 9 (1969) no. 2, pp. 221-274
[11] The exhaustion method for skew cylinders, Algebra i Analiz, Volume 12 (2000) no. 5, pp. 178-206
[12] Überlagerungen holomorph-vollständiger komplexer Räume, Arch. Math., Volume 7 (1956) no. 5, pp. 354-361
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