It is shown that the Stiefel-Whitney classes of a smooth manifold can give obstructions to realizing this manifold as the set of real points of a nonsingular real algebraic subvariety of projective space of a given dimension, even when the manifold can be embedded as an algebraic subset of real projective space of that dimension (meaning that the corresponding real algebraic variety must have complex singularities outside the real points). This strengthens earlier results by Akbulut and King. The result is an application of more technical results concerning algebraic cycles on real varieties combined with the Barth-Larsen Theorem in complex geometry.
@article{ASNSP_2009_5_8_2_267_0,
author = {Kucharz, Wojciech and van Hamel, Joost},
title = {Transcendental manifolds in real projective space and {Stiefel-Whitney} classes},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {267--277},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {2},
year = {2009},
zbl = {1174.14050},
mrnumber = {2548247},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_2_267_0/}
}
TY - JOUR AU - Kucharz, Wojciech AU - van Hamel, Joost TI - Transcendental manifolds in real projective space and Stiefel-Whitney classes JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 DA - 2009/// SP - 267 EP - 277 VL - Ser. 5, 8 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_2_267_0/ UR - https://zbmath.org/?q=an%3A1174.14050 UR - https://www.ams.org/mathscinet-getitem?mr=2548247 LA - en ID - ASNSP_2009_5_8_2_267_0 ER -
Kucharz, Wojciech; van Hamel, Joost. Transcendental manifolds in real projective space and Stiefel-Whitney classes. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 2, pp. 267-277. http://www.numdam.org/item/ASNSP_2009_5_8_2_267_0/
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