# Transcendental submanifolds of projective space

### Wojciech Kucharz

Jagiellonian University, Krakow, Poland

## Abstract

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.

## Cite this article

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

DOI 10.4171/CMH/154