Generic bifurcations of varieties

We study the zero point set of a parametrized smooth map germ. It is not only a natural generalization of Mather's theory of smooth map germs (cf. 11],12]), but also it contains the bifurcation theory of stationary solutions of parametrized ordinary differential equations. One of our main results is a classification of parametrized smooth map germs under a certain equivalence relation.Dedicated to Professor Minoru Nakaoka on his 60th birthday