2003
Mendris, Robert
Nemethi, Andras
This thesis is devoted to singularity theory. It is shown that some families of
isolated hypersurface singularities have special and surprising properties. More
precisely, we consider suspension hypersurface singularities of type
g = f (x, y) +
z n, where f is an irreducible
plane curve singularity. For such germs, we prove that the link of
g determines completely the Newton pairs of f
and the integer n except for two pathological cases, which can
be completely described. Even in the pathological cases, the link and the Milnor
number of g determine uniquely the Newton pairs of
f and n. One of the consequences of the result
is that one recovers the equisingular type of [g = 0] from its
topology, in particular, (almost) all the analytic invariants of
g. For such g , as a consequence, we obtain
Zariski's conjecture about the multiplicity. We also verify these results for a
weighted homogeneous singularity whose link is a rational homology sphere.
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