The topological structure of complex hypersurfaces with quadractic singular points

Hypersurfaces of sufficiently high degree in $\mathbb CP^{n+1}$, $n\ge3$, with fixed number and possibly fixed positions of singular points are studied. In the case where all singularities are quadratic, a topological description of such a hypersurface is given bymeans of decomposing it into a connected sum of special form. In this case, the diffeomorphism type of the hypersurface is determined by its dimension, degree, and the number of singular points. Bibl. 6 titles.