On the multiplicities of families of complex hypersurface-germs

Details On the multiplicities of families of complex hypersurface-germs On the multiplicities of families of complex hypersurface-germs

2012-02-23

arxiv.org/abs/1202.5177v2

Mathematics

Algebraic Geometry

6 pages 0 figure

Scientific paper

We show that the possible drop in multiplicity in a polynomial 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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