Hypersurfaces of sufficiently high degree in ℂPⁿ⁺¹, n ≥ 3, 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 by means 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.