Commentarii Mathematici Helvetici


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Volume 84, Issue 1, 2009, pp. 127–134
DOI: 10.4171/CMH/154

Published online: 2009-03-31

Transcendental submanifolds of projective space

Wojciech Kucharz[1]

(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