The Milnor fibre signature is not semi-continuous

Details The Milnor fibre signature is not semi-continuous The Milnor fibre signature is not semi-continuous

2009-07-30

arxiv.org/abs/0907.5252v3

Mathematics

Algebraic Geometry

Final version, to appear in "Contemporary Mathematics" volume (proceedings of Li60ber). 5 pages, uses curves.sty. A reference

Scientific paper

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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