Abstract
Suppose F: (Cn+1 × Cp, 0) → (C, 0) is a germ of a holomorphic function, and (S, 0) ⊂ (Cn+1, 0) is a germ of some hypersurface in (Cn+1, 0). The quasicaustic Q(F) of F is defined as Q(F) = {a ∈ Cp; 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.
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