Transcendental submanifolds of projective space (Q1001224)

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 \(c\).