The Milnor fibre signature is not semi-continuous
Algebraic Geometry
2010-10-21 v3
Abstract
Consider the germ of an isolated surface singularity in . 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