We provide a simple characterization of codimension two submanifolds of that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when . If the codimension two submanifold is a nonsingular algebraic subset of whose Zariski closure in is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in .
Nous fournissons une caractérisation simple des variétés de codimension deux de qui sont de type algébrique, et employons ce critère pour fournir des exemples des sous-variétés transcendantales quand . Si la sous-variété de codimension deux est un sous-ensemble algébrique non singulier de dont la fermeture de Zariski dans est un ensemble algébrique complexe non singulier, alors ce doit être une intersection algébrique complète dans .
Keywords: Smooth manifold, algebraic set, isotopy, complete intersection, vector bundle
Mot clés : variétés différentiables, ensemble algébrique, isotopie, intersection complète, fibré vectoriel
@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}, pages = {1479--1488}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {4}, year = {2010}, doi = {10.5802/aif.2561}, zbl = {1195.14076}, mrnumber = {2722248}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2561/} }
TY - JOUR AU - Kucharz, Wojciech AU - Simanca, Santiago R. TI - Codimension two transcendental submanifolds of projective space JO - Annales de l'Institut Fourier PY - 2010 SP - 1479 EP - 1488 VL - 60 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2561/ DO - 10.5802/aif.2561 LA - en ID - AIF_2010__60_4_1479_0 ER -
%0 Journal Article %A Kucharz, Wojciech %A Simanca, Santiago R. %T Codimension two transcendental submanifolds of projective space %J Annales de l'Institut Fourier %D 2010 %P 1479-1488 %V 60 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2561/ %R 10.5802/aif.2561 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2561/
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