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arXiv · 1202.5177

On the multiplicities of families of complex hypersurface-germs

Camille Plenat·David Trotman
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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 $f + tg + t^2h$ if the singular set of the tangent cone of $\{f = 0}$ is not contained in the tangent cone of $\{h = 0}$.

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Camille Plenat, David Trotman. 2012-02-23. On the multiplicities of families of complex hypersurface-germs. https://arxiv.org/abs/1202.5177

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