GLUING OF SINGULAR AND CRITICAL-POINTS

We suggest an approach to construction of algebraic hypersurfaces with given collection of singular points and polynomials with given collec tion of critical points. The approach is based on the Viro method of g luing polynomials and on the geometry of equisingular and equicritical strata in spaces of polynomials. As application we construct cuspidal plane curves of small degrees and real polynomials in two variables w ith given numbers of degenerate and non-degenerate critical points. (C ) 1997 Elsevier Science Ltd.