On the connected sum decomposition of complex hypersurfaces with quadratic singularities

We study the global topological structure of hypersurfaces in $\mathbb CP^{n+1}$, $n\ge3$, with quadratic singularities and prescribed set of singular points. Under certain restrictions on the degree, we give a precise topological description of such a hypersurface by means of decomposing it into a connected sum. In this case, the topological type of the hypersurface is determined by its dimension, degree, and the number of singular points.