On spherical cycles in the complement to complex hypersurfaces

It is known due to S. Yu. Nemirovski, that for $n\geq3$ and generic hypersurface $V\subset\mathbb C^n$ of degree $d\geq3$ there exists a sum of the Whitney spheres homotopic to an embedded sphere, which represents a nontrivial homological class of the homology group $H_n(\mathbb C^n\setminus V)$. We discuss whether a linear combination of the Whitney spheres can be represented as an embedded sphere.