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.
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Wojciech Kucharz, Transcendental submanifolds of projective space. Comment. Math. Helv. 84 (2009), no. 1, pp. 127–134