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Invariants of Newton non-degenerate surface singularities

Published online by Cambridge University Press:  17 July 2007

Gábor Braun  and
András Némethi
Gábor Braun
Affiliation:
Alfréd Rényi Institute of Mathematics, 1053 Budapest, Reáltanoda u. 13–15, Hungary braung@renyi.hu
András Némethi
Affiliation:
Alfréd Rényi Institute of Mathematics, 1053 Budapest, Reáltanoda u. 13–15, Hungary nemethi@renyi.hu
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Abstract

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We recover the Newton diagram (modulo a natural ambiguity) from the link for any surface hypersurface singularity with non-degenerate Newton principal part whose link is a rational homology sphere. As a corollary, we show that the link determines the embedded topological type, the Milnor fibration, and the multiplicity of such a germ. This proves (an even stronger version of) Zariski's conjecture about the multiplicity for such a singularity.

Keywords

hypersurface singularitieslinks of singularitiesresolution graphsNewton boundaryNewton polyhedrons14J1714Q10 (primary)52B20 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 4 , July 2007 , pp. 1003 - 1036
Copyright
Foundation Compositio Mathematica 2007