Codimension two transcendental submanifolds of projective space

Kucharz, Wojciech; Simanca, Santiago R.

Kucharz, Wojciech; Simanca, Santiago R.

Annales de l'Institut Fourier, Volume 60 (2010) no. 4, p. 1479-1488

Abstract
Résumé

We provide a simple characterization of codimension two submanifolds of $ℙ^{n} (ℝ)$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n \geq 6$ . If the codimension two submanifold is a nonsingular algebraic subset of $ℙ^{n} (ℝ)$ whose Zariski closure in $ℙ^{n} (ℂ)$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in $ℙ^{n} (ℝ)$ .

Nous fournissons une caractérisation simple des variétés de codimension deux de $ℙ^{n} (ℝ)$ qui sont de type algébrique, et employons ce critère pour fournir des exemples des sous-variétés transcendantales quand $n \geq 6$ . Si la sous-variété de codimension deux est un sous-ensemble algébrique non singulier de $ℙ^{n} (ℝ)$ dont la fermeture de Zariski dans $ℙ^{n} (ℂ)$ est un ensemble algébrique complexe non singulier, alors ce doit être une intersection algébrique complète dans $ℙ^{n} (ℝ)$ .

MR 2722248 | Zbl 1195.14076

DOI : https://doi.org/10.5802/aif.2561
Classification: 14P25, 57R22, 57R52
Keywords: Smooth manifold, algebraic set, isotopy, complete intersection, vector bundle

@article{AIF_2010__60_4_1479_0,
     author = {Kucharz, Wojciech and Simanca, Santiago R.},
     title = {Codimension two transcendental submanifolds of projective space},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {4},
     year = {2010},
     pages = {1479-1488},
     doi = {10.5802/aif.2561},
     mrnumber = {2722248},
     zbl = {1195.14076},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_4_1479_0}
}

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/item/AIF_2010__60_4_1479_0/

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