Commentarii Mathematici Helvetici
Full-Text PDF (86 KB) | Metadata | Table of Contents | CMH summary
Published online: 2009-03-31
Transcendental submanifolds of projective spaceWojciech Kucharz (1) Jagiellonian University, Krakow, Poland
Given integers m and c satisfying m − 2 ≥ c ≥ 2, we explicitly construct a nonsingular m-dimensional algebraic subset of ℙm + c(ℝ) that is not isotopic to the set of real points of any nonsingular complex algebraic subset of ℙm + c(ℂ) defined over ℝ. The first examples of this type were obtained by Akbulut and King in a more complicated and nonconstructive way, and only for certain large integers m and c.
Keywords: Smooth manifold, algebraic set, isotopy
Kucharz Wojciech: Transcendental submanifolds of projective space. Comment. Math. Helv. 84 (2009), 127-134. doi: 10.4171/CMH/154