ON QUASICAUSTICS AND THEIR LOGARITHMIC VECTOR-FIELDS

Suppose F: (C(n+1) x C(p), 0) --> (C, 0) is a germ of a holomorphic function, and (S, 0) subset-of (C(n+1), 0) is a germ of some hypersurface in (C(n+1), 0). The quasicaustic Q(F) of F is defined as Q(F) = {a is-an-element-of C(p); F(., a) has a critical point on S]. We investigate the structure of quasicaustics corresponding to boundary singularities. The procedure for calculating the modules of logarithmic vector fields is given. The minimal set of generators for the Whitney's cross-cap singular variety is explicitly calculated.