Homology and cohomology of hypersurfaces with quadratic singular points in generic position (Q1303356)

The author is mainly interested in hypersurfaces with quadratic singularities and calculates the homology groups of such hypersurfaces. The author uses this calculation to give a topological description of such a hypersurface by means of decomposing it into a connected sum. As a consequence the topological type of the hypersurface is determined by its dimension, degree, and the number of singular points. Note that although the author deals with quadratic singularities, all results obtained can be extended to the case of arbitrary isolated singularities.