Kucharz, Wojciech Transcendental submanifolds of projective space. (English) Zbl 1209.57023 Comment. Math. Helv. 84, No. 1, 127-134 (2009). Summary: Given integers \(m\) and \(c\) satisfying \(m - 2 \geq c \geq 2\), we explicitly construct a nonsingular \(m\)-dimensional algebraic subset of \(\mathbb P^{m + c}(\mathbb R)\) that is not isotopic to the set of real points of any nonsingular complex algebraic subset of \(\mathbb P^{m + c}(\mathbb C)\) defined over \(\mathbb R\). 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 \(c\). Cited in 3 Documents MSC: 57R55 Differentiable structures in differential topology 14P25 Topology of real algebraic varieties Keywords:smooth manifold; algebraic set; isotopy PDFBibTeX XMLCite \textit{W. Kucharz}, Comment. Math. Helv. 84, No. 1, 127--134 (2009; Zbl 1209.57023) Full Text: DOI Link