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arXiv · 0907.5252

The Milnor fibre signature is not semi-continuous

Dmitry Kerner·Andras Nemethi
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Abstract

Consider the germ of an isolated surface singularity in $(\mC^3,0)$. The corresponding Milnor fibre possesses the homology lattice (the integral middle homology with a natural symmetric intersection form). An old question of A.Durfee (1978) asks: is the signature of this form non-increasing under degenerations? The present article answers negatively: We give examples of Newton non-degenerate families where the signature increases under degeneration.

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Dmitry Kerner, Andras Nemethi. 2009-07-30. The Milnor fibre signature is not semi-continuous. https://arxiv.org/abs/0907.5252

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