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On quasicaustics and their logarithmic vector fields

Published online by Cambridge University Press:  17 April 2009

S. Janeczko
S. Janeczko
Affiliation:
Institute of Mathematics, Technical University of Warsaw, Pl. Jednosci Robotniczej 1, 00-661 Warsaw, Poland
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 365 - 376
Copyright
Copyright © Australian Mathematical Society 1991

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