On the multiplicities of families of complex hypersurface-germs

Abstract

We show that the possible drop in multiplicity in an analytic family $F(z,t)$ of complex analytic hypersurface singularities with constant Milnor number is controlled by the powers of $t$. We prove equimultiplicity of $\mu$-constant families of the form $f+tg+t^{2}h$ if the singular set of the tangent cone of $\{f = 0}$ is not contained in the tangent cone of $\{h = 0}$.

arXiv comment6 pages 0 figure

Cited by in corpus (1)

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