Codimension two transcendental submanifolds of projective space

Kucharz, Wojciech, and Simanca, Santiago R.. "Codimension two transcendental submanifolds of projective space." Annales de l’institut Fourier 60.4 (2010): 1479-1488. <http://eudml.org/doc/116310>.

@article{Kucharz2010,
abstract = {We provide a simple characterization of codimension two submanifolds of $\{\mathbb\{P\}\}^n(\{\mathbb\{R\}\})$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n\ge 6$. If the codimension two submanifold is a nonsingular algebraic subset of $\{\mathbb\{P\}\}^n(\{\mathbb\{R\}\})$ whose Zariski closure in $\{\mathbb\{P\}\}^n(\{\mathbb\{C\}\})$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in $\{\mathbb\{P\}\}^n(\{\mathbb\{R\}\})$.},
affiliation = {Jagiellonian University Institute of Mathematics Lojasiewicza 6 30-348 Krakow (Poland); University of New Mexico Department of Mathematics & Statistics Albuquerque, NM 87131 (USA)},
author = {Kucharz, Wojciech, Simanca, Santiago R.},
journal = {Annales de l’institut Fourier},
keywords = {Smooth manifold; algebraic set; isotopy; complete intersection; vector bundle; smooth manifold},
language = {eng},
number = {4},
pages = {1479-1488},
publisher = {Association des Annales de l’institut Fourier},
title = {Codimension two transcendental submanifolds of projective space},
url = {http://eudml.org/doc/116310},
volume = {60},
year = {2010},
}

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
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 4
SP - 1479
EP - 1488
AB - We provide a simple characterization of codimension two submanifolds of ${\mathbb{P}}^n({\mathbb{R}})$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n\ge 6$. If the codimension two submanifold is a nonsingular algebraic subset of ${\mathbb{P}}^n({\mathbb{R}})$ whose Zariski closure in ${\mathbb{P}}^n({\mathbb{C}})$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in ${\mathbb{P}}^n({\mathbb{R}})$.
LA - eng
KW - Smooth manifold; algebraic set; isotopy; complete intersection; vector bundle; smooth manifold
UR - http://eudml.org/doc/116310
ER -