Picard-Lefschetz Monodromy Groups of Quadratic Hypersurfaces

We study the topology of the space of affine hyperplanes $L\subset {\text{CC}}^n$ which are in general position with respect to a given generic quadratic hypersurface $A$, and calculate the monodromy action of the fundamental group of this space on the relative homology groups $H_{\ast }({\text{CC}}^n,A\cup L)$ associated with such hyperplanes.