English

The Milnor fibre signature is not semi-continuous

Algebraic Geometry 2010-10-21 v3

Abstract

Consider the germ of an isolated surface singularity in (\mC3,0)(\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.

Keywords

Cite

@article{arxiv.0907.5252,
  title  = {The Milnor fibre signature is not semi-continuous},
  author = {Dmitry Kerner and Andras Nemethi},
  journal= {arXiv preprint arXiv:0907.5252},
  year   = {2010}
}

Comments

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