Embedding subsets of tori Properly into 2
[Plongement propre dans 2 de sous-ensembles de tores]
Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1537-1555.

Nous avons fait des progrès sur le problème du plongement des surfaces de Riemann ouvertes dans 2 . Il est connu que pour tout entier naturel d2, le nombre N d :=3d 2+1 est le plus petit entier naturel pour lequel il existe un plongement propre de toute variété de Stein de dimension d dans N d . Le problème du plongement propre des variétés de Stein de dimension 1 dans 2 reste ouvert (il existe du plongement propre dans 3 ). Dans ce texte nous prouvons le résultat suivant  : soit 𝕋 un tore complexe de dimension 1  ; alors il existe un plongement propre de toute partie de 𝕋, dont la frontière a un nombre fini de composantes (aucune d’elle n’étant un point), dans 2 . Nous prouvons aussi que les algèbres de fonctions analytiques sur certaines surfaces de Riemann sont doublement générées.

Let 𝕋 be a complex one-dimensional torus. We prove that all subsets of 𝕋 with finitely many boundary components (none of them being points) embed properly into 2 . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.

DOI : https://doi.org/10.5802/aif.2305
Classification : 32H35,  30F99
Mots clés : plongements holomorphiques, surfaces de Riemann
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     author = {Wold, Erlend Forn{\ae}ss},
     title = {Embedding subsets  of tori {Properly} into $\mathbb{C}^2$},
     journal = {Annales de l'Institut Fourier},
     pages = {1537--1555},
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Wold, Erlend Fornæss. Embedding subsets  of tori Properly into $\mathbb{C}^2$. Annales de l'Institut Fourier, Tome 57 (2007) no. 5, pp. 1537-1555. doi : 10.5802/aif.2305. http://archive.numdam.org/articles/10.5802/aif.2305/

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