On the homology of a perturbation of a complex projective hypersurfaces

A nonsingular hypersurface $X$ in $\mathbb CP^{n+1}$ with $n\ge3$ are studied. We state a theorem saying that the homology coming from the affine part of a hypersurface of smaller degree forms a durect summand in the homology of $X$, which is independent over integers with the class of the multiple hyperplane section. The proof is outlined.