Codimension two transcendental submanifolds of projective space
Annales de l'Institut Fourier, Volume 60 (2010) no. 4, pp. 1479-1488.

We provide a simple characterization of codimension two submanifolds of n () that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when n6. If the codimension two submanifold is a nonsingular algebraic subset of n () whose Zariski closure in n () is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in n ().

Nous fournissons une caractérisation simple des variétés de codimension deux de n () qui sont de type algébrique, et employons ce critère pour fournir des exemples des sous-variétés transcendantales quand n6. Si la sous-variété de codimension deux est un sous-ensemble algébrique non singulier de n () dont la fermeture de Zariski dans n () est un ensemble algébrique complexe non singulier, alors ce doit être une intersection algébrique complète dans n ().

DOI: 10.5802/aif.2561
Classification: 14P25,  57R22,  57R52
Keywords: Smooth manifold, algebraic set, isotopy, complete intersection, vector bundle
Kucharz, Wojciech 1; Simanca, Santiago R. 2

1 Jagiellonian University Institute of Mathematics Lojasiewicza 6 30-348 Krakow (Poland)
2 University of New Mexico Department of Mathematics & Statistics Albuquerque, NM 87131 (USA)
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Kucharz, Wojciech; Simanca, Santiago R. Codimension two transcendental submanifolds of projective space. Annales de l'Institut Fourier, Volume 60 (2010) no. 4, pp. 1479-1488. doi : 10.5802/aif.2561. http://www.numdam.org/articles/10.5802/aif.2561/

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