[Sur uniformisation simultanée et nonuniformisabilité locale]
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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Alexey Glutsyuk 1
@article{CRMATH_2002__334_6_489_0, author = {Alexey Glutsyuk}, 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}, }
Alexey Glutsyuk. On simultaneous uniformization and local nonuniformizability. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 489-494. doi : 10.1016/S1631-073X(02)02268-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02268-9/
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